Had a little thought exercise where I was trying to design a character who crammed the most possible types of damage resistances into it using only racial abilities, class features, and feats.  For the purposes of this I'm only looking at effects that are always on, not limited use instances like Barbarian Rage or the Gift of the Chromatic Dragon feat.  I'm also ignoring resistance to spell damage from the Abjurer and Oath of the Ancients since that isn't a single damage type and is difficult to quantify.

What I came up with was a tiefling Storm Soul Sorcerer 6/Necromancer 10.  That combination gives you resistance to fire, lightning, thunder, and necrotic damage.  Take the Gate Warden or Planar Philosopher background to get Scion of the Outer Planes and choose Lawful, Upper, or the Outlands to get resistance to force, radiant, or psychic damage.  Then pick up Infernal Constitution for resistance to cold and poison damage, and Planar Wanderer to round yourself out with acid resistance.  That's permanent resistance to eight damage types.

Anyone come up with builds that can beat that?

You could swap necromancer wizard 10's necrotic resistance for dao genie warlock 6's bludgeoning resistance. Still the same number of resistances, but sooner and more common.

Good thinking.

Level 20 monk gets resistance to all but force damage and invisibility to boot for the first minute of every fight. 

Not a permanent effect, does not count.  [REDACTED]

Paladin 20, Oath of Conquest - you have resistance to ALL damage. The warlock/Sorceror gets a whack at 12th level and granted this is 20th but you wanted "better" not quicker :)

This is kind of stretching the rules a bit on the definition of "always on" but a level 20 Warforged Bear Totem Barbarian with the Scion of the Outer planes feat (the Outlands) have resistances to ALL damage types and immunity to disease. Since they are a level 20 barbarian they have unlimited rages and so they can be resitant "all the time". Being warforged they can stay vigilant even during long rests and thus can keep the resistances up pretty much for forever. And they can't be put to sleep using magic either. :)

Quote from Estaln >>

Paladin 20, Oath of Conquest - you have resistance to ALL damage. The warlock/Sorceror gets a whack at 12th level and granted this is 20th but you wanted "better" not quicker :)

 Except that I specified permanent resistances and the paladin only gets it for 1 minute/day.  Otherwise, all that would be required is a Totem Warrior Barbarian with Scion of the Outer Planes to get psychic resistance who selects Bear Totem at 3rd level.

Abjurer gets resistance to all spell damage at level 14.  Does not include non-magic, but resistance is resistance

Quote from 6thLyranGuard >>

Had a little thought exercise where I was trying to design a character who crammed the most possible types of damage resistances into it using only racial abilities, class features, and feats.  For the purposes of this I'm only looking at effects that are always on, not limited use instances like Barbarian Rage or the Gift of the Chromatic Dragon feat.  I'm also ignoring resistance to spell damage from the Abjurer and Oath of the Ancients since that isn't a single damage type and is difficult to quantify.

If infusions count (they are magic items, but they're also class features) you can hit 9

• Tiefling: Fire
• Infernal Constitution: poison, cold
• Scion of the Outer Planes (L): force
• Planar Wanderer: acid
• Storm Sorcerer-6: lightning, thunder
• Artificer-6 (resistant armor infusion): necrotic
• Warlock-6 (celestial): radiant. Or Warlock-6(genii dao): bludgeoning.

Using the Scaled Toughness draconic gift you could  get resistance to piercing and slashing damage. Using a supernatural gift from Mythic Odysseys of Theros you can get a resistance to poison damage with Anvilwrought, resistance to psychic damage with Inscrutable, or best of all a resistance to necrotic and radiant damage with Nyxborn.

With epic boons you can get Boon of Resilience giving resistance to bludgeoning, piercing, and slashing damage from nonmagical weapons. Which is technically ann improvement you can also get immunity to poison, thunder, lightning, and fire damage.

Debatably you might be able to use Reincarnate to get another race and keep Infernal Constitution solely due to the fact there’s no rule for losing feats (to my knowledge) and it not being racial trait. Dragonborn is the only on that matters and you need to get the Ember of the Fire Giant feat to restore your fire resistance. Drakewarden ranger and fiend warlock likely have potential. Blood Hunter: Order of the Ghostslayer has resistance to necrotic damage at level 3 which is interesting

if you pick a 2024 tiefling(infernal) and go oath of ancients pally. You get fire resistantance from infernal tiefling, then at 4 pick infernal constitution to pick up cold and poison. then at level 7 you get necrotic, radiance and psycic from their warding. so you would have fire, cold, poison, necrotic, radiance, psychic, and if you happen to pick up a brooch of shielding, youd have force also.

OK, I',m a bit late to this but if anyone is still interested, assuming total of 20 levels how about:

Aasimar (Volo's Guide to Monsters) for Resistance to Necrotic and Radiant damage,

The aforementioned Planar Philosopher or Gate Warden to get Scion of the Outer Planes (Planescape Adventures in the multiverse) as a background for Resistance to Force or Psychic damage,

Then 6 levels of Storm Sorcerer (Xanathars Guide to Everything) for Resistance to Lightning and Thunder damage.

Followed by 6 levels of Marid Genie Warlock (Tasha's Cauldron of Everything for Resistance to Cold damage.

And then 6 levels of Forge Cleric (Xanathars Guide to Everything) for Resistance to Fire.

For Feats; Dungeon Delver (PHB) for Resistance to damage from traps, Poisoner (Tasha's Cauldron of Everything) for Resistance to Poison damage,

That should bring you to 8 specific damage resistances (Cold, Fire, Lightning, Necrotic, Poison, Psychc or Force, Radiant and Thunder) and one that is a bit niche (traps). And you have 2 spare levels and feats to play with.

EDIT: I missed the Planar Warrior feat noted above for Resistance to Acid Damge so it's upto 9 specific resistances!

Oath of Redemption Paladin, level 20 feature. Technically it's not permanent, but just don't attack and...