See above. Some of my favorites are

fire rune/unarmed fighter/ Rune Knight/ Simic Hybrid/ Grappling Tentacles. Averages about 40 damage per turn and you get to use a fun race. Playing a Artificer (Armorer) 6/ Fighter (Rune Knight) 4 and it’s been really fun. Also diffuses PVP quickly (EG: They’re on death saves after action surge)

Ranger anything. Controversial, but Ranger is good, just not top tier (maybe 6th most powerful). People hate on it because it is bad out of combat. Just look at gloom stalker or hunter (coloss slayer) for examples in combat. Even horizon walker is good.

Paladin (Oath of Conquest) 5/ Warlock (Hexblade/Pact of the blade) 5. This can average very good damage.

**Healerbot alert** Cleric (Peace or Life) 2, Monk (Way of Mercy) 3. Very nice for role play aesthetic for the backstory. It gives thoughts on how you could have been a monk that isn’t a frontline fighter, but rather someone that helps others and can still pack a punch. As an example, Grandmaster Kane from The Legend of Drizzt.

Kobold Rune Knight 18/Graviturgist 2 with a spell scroll of enlarge/reduce.

Result:  25 pound kobold casts reduce and uses adjust density on itself, becoming 1.5625 pounds, then uses Runic Juggernaut. 

While your DM may have specific feelings about how tall and thicc a Huge kobold is, the kobold should become substantially less dense than helium, and finally be able to do what it always wanted: fly!  Recommend tying the kobold to a basket, hopping in, and casting create bonfire to keep the poor guy warm.

Moon Druid X/Paladin 2 (Aasimar)- Smite with natural weapons and full caster slots. It's a little MAD but you can keep Cha and Str on 13.

Combine that one with Aasimar and you got yourself some holy bear flavor. Go smite them with your paws!

Wildshaped druids can't cast spells, but otherwise retain their class and race features. There's various class features you might pick up that feel like spells, but don't actually involve casting a spell... for example, the Radiant Sun Bolt laser beam that a Sun Soul monk fires in place of unarmed strikes, and even it's level 11 Searing Sunburst kamehameha! Most Beasts that you'll find to shape into aren't likely to have more than a 16 Dexterity, maybe 18 at the most, so you won't be shooting out Sun Bolts quite as well as you do as a human.... but Monk Unarmored Defense does usually cause a Beast forms AC to jump up several points, and in general a lot of the Monk features (enhanced movement speed, deflect missiles, evasion, str-based martial arts, diamond soul, etc.) feel pretty good while you're in the form of a wolf or a snake or whatever. Moon Druid 6/Sun Soul 14 could be a pretty fun way to subvert expectations (an AC 21 Ice Spider Queen that shoots lasers and throws bombs at enemies they've webbed? Or an AC 15 Cave Bear who makes four 1d8+5 Unarmed Strike attacks per round instead of its normal multiattack to roughly double its usual damage output?). Or, if you can abide losing Diamond Soul and Searing Sunburst, Moon Druid 12/Sun Soul 8, to be a more effective full-dex blaster as an Air Elemental with 20 AC and a 90 flying speed?

The Astral Self monk could be a pretty funny combination with druid as well, if you'd like your rat to grow giant muscly spectral arms that they beat people with while squeeking around :p . That subclass is probably a bit easier to optimize with Druid, since it rewards you for maximizing your Wisdom and ignoring dexterity, which synergizes well with Druid and Wild Shape (which overwrites your Dex in wild shaped form but keeps your wisdom). While shooting laser beams as a mouse is definitely flashier, being able to make a flurry of wisdom-based attacks is going to do more damage than most beasts natural weapons, while also bumping up their AC, so you're really just making all the Beast forms tankier and more lethal in a way that makes the chonky beasts very useful. 

A gnomish draconic bloodline sorcerer. 'You think me small, cretin? The blood of the mightiest of all creatures flows in my veins!' Fireball.

Fighter (battlemaster) 7, Bard (swords) 5, Warlock (tome/Archfey) 8.  Max out Charisma for Shillelaghs (acquired through tome).  You can get up to 19-20 short rest abilities (Battlemaster, flourishes, inspirations, invocations, racial abilities, etc).

Thats more than enough (usually too many) abilities per short rest.  You’ll be struggling to use them all up, analysis paralysis is a thing. 

Human variant, fighter, champion subclass. 1st level get the slasher feat. Choose between focusing on dexterity or strength, then allocate your stats to get either a 17 in strength or dexterity when adding in your slasher feat bonus and 1 human stat bump. Other human stat bump goes into constitution to start with 16 Con. Put enough points to get 13-14 charisma. Rest of pints go w/e you want, I do wisdom for saves and perception. Choose two weapon fighting style for the first few levels for damage. Use your hand axes or scimitars to use your slashing damage and two weapon fighting depending on your offensive attribute.

level 3 go champion to extend your crit range a bit to proc your slasher feat a bit more.

Level 4 choose crusher feat. This is counter intuitive for the next two levels played, but sets up a bump for either double Dex and con mod upgrade at level 6 fighter, or 18 strength now if using strength. You can also choose to wield light hammers if crush is advantageous for some reason.

Get to level 5 for extra attack. Your damage gets a slight bump, but more importantly it’s a third potential critical.

total level 6 we go one level of genie warlock and pick the Dao as our patron. We can now add crushing damage to one of our attacks once per turn. If we crit fish a little bit we can actually deal bludgeoning damage and slashing damage on the same attack roll. When you crit you can now impose disadvantage on your targets attack rolls and give everybody else advantage vs that target.

try to get 11 fighter/1 warlock for the additional attack. Make the call to go more champion for more crit range, or to go to a different class. More warlock adds utility and spells. Rogue class adds sneak die to shore up damage fall off, and really rewards the crit fishing. Swashbuckler adds to your damage and mobility options.

you can start elf or half elf to try and grab elven accuracy, but it takes quite a bit longer to get online.

I one cool combo I do is Ranger (doesn't matter what type) and the Haunted One background works great! Even better if you are multi classing as a paladin!

Astral Self 3+/Peace Domain 2+ Probably a Wood Elf

Super old, ancient elf pacifist hippie type, who walks around battle realigning chakras and healing wounds while his 'sprit self' handles the violence so he can keep his actual 'worldly' hands blood-free. 

The infamous Hexjurer.

Hexblade 1 / Abjurer X.

- Medium armor, shield prof and d8 initial HP shrug off one of the major weaknesses of Wizard in terms of AC.

- Armor of Agathys + Arcane Ward turns you a serious threat at melee distance ans gives you more durability than Fighters.

- Hexblade Curse + Magic Missile makes you a top-tier single target damage dealer.

And you still have the entire Wizard package with best in class battlefield control, utility, rituals and AoE damage spells. Everything available since low level.

Riffing on the fun uses of moon druid from Sutlo and ChickenChamp, I love adding a little something to a wildshaping druid.

Moon Druid 9/ Bladesinger 2:

Variant Human or Custom Lineage so you can have resilient (con) and max out intelligence. Moon Druids don't actually need stats other than a not terrible constitution and enough wisdom to multiclass thanks to using wildshape stats and druids having a plethora of amazing spells that don't care about wisdom. Round one cast an impactful concentration spell and activate bladesong, making it very hard to drop concentration. Round two wildshape into a Giant Snapping Turtle and start going to town biting people while enjoying a 22 AC.

Quote from Ir0ns0ul >>

The infamous Hexjurer.

Hexblade 1 / Abjurer X.

- Medium armor, shield prof and d8 initial HP shrug off one of the major weaknesses of Wizard in terms of AC.

- Armor of Agathys + Arcane Ward turns you a serious threat at melee distance ans gives you more durability than Fighters.

- Hexblade Curse + Magic Missile makes you a top-tier single target damage dealer.

And you still have the entire Wizard package with best in class battlefield control, utility, rituals and AoE damage spells. Everything available since low level.

I mean really, it seems like all you actually need in that package is Armor of Agathys. You can pick that up as a class spell by being a Mark of Warding Dwarf instead, including a non-spell-slot cast of it once per day. Or, as any other non-hexblade warlock, several of which probably have as good or better level 1 class features than Hexblade, considering you probably aren't building to take advantage of making weapon attacks with charisma. 

Wild Magic Barbarian X / War Magic Wizard 3-4

I want to play this at some point, and I find it fun because Wizards arent usually something that you think will synergize well with Barbarians. 

• Arcane Deflection gives you a bonus to AC or Saving Throw once per round (using your reaction) and can be used during your rage to improve tankiness
• Tactical Wit lets you add your Int modifier to initiative checks (at least a +1 from the multiclassing prerequisite) which works with your Feral Instinct feature to ensure you are at the top of initiative
• At level 3 you have access to 2nd level spells. Several of the spells you choose can be used to buff yourself before combat begins or as utility outside of combat. Cantrips can be chosen to either give you a ranged option to fall onto or to improve your weapon attacks (SCAG-trips) at early Barb level when you dont feel like raging
• Bolstering Magic can pair with Arcane Recovery to regain spell slots between long rests so you can make the most out of what few spells you have

Quote from Kaboom979 >>

Wild Magic Barbarian X / War Magic Wizard 3-4

I want to play this at some point, and I find it fun because Wizards arent usually something that you think will synergize well with Barbarians. 

• Arcane Deflection gives you a bonus to AC or Saving Throw once per round (using your reaction) and can be used during your rage to improve tankiness
• Tactical Wit lets you add your Int modifier to initiative checks (at least a +1 from the multiclassing prerequisite) which works with your Feral Instinct feature to ensure you are at the top of initiative
• At level 3 you have access to 2nd level spells. Several of the spells you choose can be used to buff yourself before combat begins or as utility outside of combat. Cantrips can be chosen to either give you a ranged option to fall onto or to improve your weapon attacks (SCAG-trips) at early Barb level when you dont feel like raging
• Bolstering Magic can pair with Arcane Recovery to regain spell slots between long rests so you can make the most out of what few spells you have

 I'm now picturing this massive barbarian warrior-dude... but, like four of him... because he cast Mirror Images before raging at the start of combat.

Mark of Healing Halfling + School of Abjuration Wizard

Prevent damage when you can, heal damage when you can't. 

I played an Arcane Archer 6/ Alchemist 4 lightfoot halfling, and she was the most fun multiclass I've ever done. Expeditious Retreat + range + healing + random potions = options galore. Tons of flavor, tons of utility in and out of combat, and a little emergency healing makes for a very versatile build that doesn't sacrifice DPS.

How about a Simic Hybrid Bloodhunter Mutant grappler? Fighter 1 or 2 for Unarmed Fighting Style (or you could take Fighting Initiate I suppose), Bloodhunter 3-11 (for the Potency mutation to let you reach either 22 or 24 Strength by end game), maybe a couple levels of Barbarian to rage for advantage on those checks...

For your second mutation after Bloodhunter 7, the Mobility mutation makes the Grappler feat incredibly strong, if you can cancel out the disadvantage it would ordinarily provide you on Strength checks. Being a Barbarian in a rage is one such way! As a Simic Hyrbrid, you can be grappling up to 4 creatures at once after level 5, enough to really make a Grappler build less of a one-target-threat. 

Quote from Chicken_Champ >>

How about a Simic Hybrid Bloodhunter Mutant grappler? Fighter 1 or 2 for Unarmed Fighting Style (or you could take Fighting Initiate I suppose), Bloodhunter 3-11 (for the Potency mutation to let you reach either 22 or 24 Strength by end game), maybe a couple levels of Barbarian to rage for advantage on those checks...

For your second mutation after Bloodhunter 7, the Mobility mutation makes the Grappler feat incredibly strong, if you can cancel out the disadvantage it would ordinarily provide you on Strength checks. Being a Barbarian in a rage is one such way! As a Simic Hyrbrid, you can be grappling up to 4 creatures at once after level 5, enough to really make a Grappler build less of a one-target-threat. 

 On a similar but tangential note, pairing 7 levels of the Oath of the Open Seas Paladin subclass from D&D beyond with the Grappler feat is incredibly powerful for part of a grappler build, because your aura lets you ignore effects which would restrain you, allowing you to "pin" someone without impeding your own movement. Add in some Barbarian for advantage on Athletics checks and you're all set. The downside to a Paladin/Barb multiclass is it may be a bit MAD. Str and Con will be good for both, but you will also need a decent Charisma score and possibly Dex as well if you plan to not wear heavy armor

Edit: Thinking about it more, the best barb multiclass for this might be the Battlerager. Your spiked armor deals damage on a successful grapple, can be used to make a bonus action attack, and the spikes count as a weapon (so can be used for divine smite???). 

I've never valued Battlerager very high, because usually its better to build a grappler wearing plate as a fighter, grapplers have other uses of their bonus action that they often prefer, and usually you aren't actually "using the Attack action to grapple" but rather a Bonus Action from Tavern Brawler, Grappling Strike, or another feature like the Simic's tentacles. Playing around with a Simic Grappler, I think that Rune Knight is probably a better way to find advantage on strength checks than a Barbarian's rage is... but I will hand it to the Battlerager, the ability to wield a weapon that doesn't require a hand might be its one (small) point in its favor. 

I will say though... dropping Bloodhunter in exchange for that Paladin caps you at 20 strength, and isn't as thematic with the tentacle mutant angle, but does streamline your features quite a bit. I think that a Rune Knight 12/Open Seas 8 grappler would be pretty effective.