Great Weapon Master is probably the #1 choice of barbs, but you might also consider Sentinel, Charger, Mobile, Polearm Master, Slasher, Fighting Initiate, and Orcish Fury (for orcs, half-orcs). It really depends on your style of play.
It depends a lot on what your goals are for the character; there is a lot of focus online on Great Weapon Master or Polearm Master, as both allow you to reliably do more damage, and a lot of "optimal" builds try to take both. However, this is building a Barbarian for damage, and arguably if that's your priority then Fighter is the better class for that, though there's rarely any harm in dealing more damage as long as you're still keeping your allies safe.
If you want to focus more on tanking then Sentinel is a good choice as it makes it easier to pin enemies down so they can only really fight you.
Slasher can somewhat do this too while being a half feat, though personally I'd be tempted to go for Crusher and a maul instead, as being able to shunt an enemy 5 feet is actually a really powerful ability as you can move an enemy away from an ally so they don't need to Disengage to move away, and it lets you position them for opportunity attacks if they try to follow, you can also use it to push towards hazards or area spells. Plus if you get a critical you can pseudo-stun the target (give everyone advantage to hit it).
I'd also point to Shield Master as a sometimes overlooked feat for a Barbarian; a sword and board Barbarian can be very tough, and a bonus action Shove lets you knock an enemy prone which will slow them considerably (and can give allies advantage to hit them), and as a Barbarian you get advantage to Strength checks while Raging. It also makes you very strong against Dexterity save effects. This one will depend a lot on how your DM treats tanking however, as a higher AC could deter enemies from attacking you, even if you use Reckless Attack a lot, but if your DM is happy to have enemies seek the advantage Reckless Attacks give then it could work well.
The Dragon of Louis is in town! Time for some words of wisdom.
Okay, so you definitely want GWM. Not just for the tradeoff(attack-5, damage+10) but also cleaver is helpful. Next, unless you're playing a battlerager, I recommend you go ahead and try Polearm Master and Sentinel. Not only can you lock down the battlefield like this, but you can reckless attack with very little consequences! Just reckless from 10 feet away (15 for a bugbear, and that's a lot) and then step back 5 feet. If they try to claim their advantage, they are stopped dead by sentinel and polearm master; if they try to run away, then you can chase them with a +10 movement speed. Finally, a free bonus action attack is really nice, which polearm master gives. Plus, you can GWM your bonus action attack, which you should always try to do.
If you're a totem barbarian, and at level 6 chose the Eagle totem for the vision out to 1 mile: Observant and Keen Mind can be really useful, but this puts you at risk of having a Barbarian Character who is useful outside of combat as well as in combat.
Savage Attacker is usually considered one of the worst feats in the game. However, if you're playing a high level Barbarian and you've got a few dice worth of Brutal Critical, the Savage Attacker feat will give you a re-roll when your critical hit dice wimp out on you. It may be a crap feat when your weapon damage is only a d12 (we know you're wielding a greataxe) but when you're rolling 3d12 or 4d12, re-rolling a bad crit result can be a game-changer.
Rollback Post to RevisionRollBack
Behind every successful Warlock, there's an angry mob.
Savage Attacker only lets you reroll the weapon's damage dice, not damage dice from crits, special abilities, or spells. If that's what you want it for, you'd be better off taking the Fighting Style (Great Weapon) feat so that you can get a reroll any time you roll a 1 or 2 instead of just using a 1/day reroll.
But I'd honestly choose a different feat over either of those. One feat I'm not seeing people mention here is Resilient (Wisdom). Definitely a good feat for a melee character.
Parroting most of what's already recommended by previous posters.
Great Weapon Master: you're already resistant to most weapon attacks so might as well make reckless attacks for some sweet damage. CC is good but the best CC is a dead enemy.
Polearm Master: Your character will get access to Bonus Action: Attack. Barbarians arguably gets the most benefit from this one since they're not that much worst off with the lower AC from lack of shield and they get the minimum of +2 damage from rage.
Duelling: If taking a -5 accuracy for more damage is not your thing then Duelling for a straight +2 on top of your STR MOD and minimum of +2 from Rage might suit your play style more. At 20 STR you'll be adding + 9 on top of your damage die each hit. Try to get your hands on a longsword Flametoungue or similar items for stupid levels of damage.
If not taking Bear Totem Barbarian then consider taking the Gift of the Chromatic Dragon feat at some point. It allows you to do something with your bonus action, gives your attacks a little but of elemental damage while giving you resistance to an element at the cost of a reaction.
Flavor-wise: take the Tavern Brawler Feat, now you can use your enemies as your weapons after you grapple them
Ritual Caster: if your party is made up of all martial characaters
Skill Expert: if you want to add more prof bonus to your Athletics Grapple checks without dipping to other classes
Tough for more Tanky-ness
Sentinel is a Meh for Barbarian since you're better off selecting ASI to STR, DEX or CON
Resilient WIS: since being CC'd for half the fight is not fun.
Gonna give you something OTHER THAN GWM - a feat my barb9/fighter6 does not actually have. As someone else mentioned, if your focus is to maximize melee damage, a fighter is probably the better choice. Instead, my bard is more about taking damage (with awareness of the tank fallacy). I use a shield and trident.
One of my fave for my totem barb is Gift of the Chromatic Dragon. I get a low use (too many other BA options) 1d4 pick of elemental damage types but the main benefit is the 5 per day reactive resistance to elemental damage. This allows me to use my totem for Wolf to grant pact tactics to my party and still get the best features of bear totem.
Wat feats are good for a barbarian to pick up?
What feats are replacable and what would you replace them with?
Great Weapon Master is probably the #1 choice of barbs, but you might also consider Sentinel, Charger, Mobile, Polearm Master, Slasher, Fighting Initiate, and Orcish Fury (for orcs, half-orcs). It really depends on your style of play.
It depends a lot on what your goals are for the character; there is a lot of focus online on Great Weapon Master or Polearm Master, as both allow you to reliably do more damage, and a lot of "optimal" builds try to take both. However, this is building a Barbarian for damage, and arguably if that's your priority then Fighter is the better class for that, though there's rarely any harm in dealing more damage as long as you're still keeping your allies safe.
If you want to focus more on tanking then Sentinel is a good choice as it makes it easier to pin enemies down so they can only really fight you.
Slasher can somewhat do this too while being a half feat, though personally I'd be tempted to go for Crusher and a maul instead, as being able to shunt an enemy 5 feet is actually a really powerful ability as you can move an enemy away from an ally so they don't need to Disengage to move away, and it lets you position them for opportunity attacks if they try to follow, you can also use it to push towards hazards or area spells. Plus if you get a critical you can pseudo-stun the target (give everyone advantage to hit it).
I'd also point to Shield Master as a sometimes overlooked feat for a Barbarian; a sword and board Barbarian can be very tough, and a bonus action Shove lets you knock an enemy prone which will slow them considerably (and can give allies advantage to hit them), and as a Barbarian you get advantage to Strength checks while Raging. It also makes you very strong against Dexterity save effects. This one will depend a lot on how your DM treats tanking however, as a higher AC could deter enemies from attacking you, even if you use Reckless Attack a lot, but if your DM is happy to have enemies seek the advantage Reckless Attacks give then it could work well.
Characters: Bullette, Chortle, Dracarys Noir, Edward Merryspell, Habard Ashery, Legion, Peregrine
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I'm a big fan of Polearm Master + Great Weapon Master + Sentinel feats
Great Weapon Master is a must.
The Dragon of Louis is in town! Time for some words of wisdom.
Okay, so you definitely want GWM. Not just for the tradeoff(attack-5, damage+10) but also cleaver is helpful. Next, unless you're playing a battlerager, I recommend you go ahead and try Polearm Master and Sentinel. Not only can you lock down the battlefield like this, but you can reckless attack with very little consequences! Just reckless from 10 feet away (15 for a bugbear, and that's a lot) and then step back 5 feet. If they try to claim their advantage, they are stopped dead by sentinel and polearm master; if they try to run away, then you can chase them with a +10 movement speed. Finally, a free bonus action attack is really nice, which polearm master gives. Plus, you can GWM your bonus action attack, which you should always try to do.
DMing:
The Cataclysm Stadium
Rise of the White Mask
Optimization Guides:
Literally Too Angry to Die - A Guide to Optimizing a Barbarian.
Obscure feat choices:
If you're a totem barbarian, and at level 6 chose the Eagle totem for the vision out to 1 mile: Observant and Keen Mind can be really useful, but this puts you at risk of having a Barbarian Character who is useful outside of combat as well as in combat.
Blank
Savage Attacker is usually considered one of the worst feats in the game. However, if you're playing a high level Barbarian and you've got a few dice worth of Brutal Critical, the Savage Attacker feat will give you a re-roll when your critical hit dice wimp out on you. It may be a crap feat when your weapon damage is only a d12 (we know you're wielding a greataxe) but when you're rolling 3d12 or 4d12, re-rolling a bad crit result can be a game-changer.
Behind every successful Warlock, there's an angry mob.
Savage Attacker only lets you reroll the weapon's damage dice, not damage dice from crits, special abilities, or spells. If that's what you want it for, you'd be better off taking the Fighting Style (Great Weapon) feat so that you can get a reroll any time you roll a 1 or 2 instead of just using a 1/day reroll.
But I'd honestly choose a different feat over either of those. One feat I'm not seeing people mention here is Resilient (Wisdom). Definitely a good feat for a melee character.
Find your own truth, choose your enemies carefully, and never deal with a dragon.
"Canon" is what's factual to D&D lore. "Cannon" is what you're going to be shot with if you keep getting the word wrong.
Parroting most of what's already recommended by previous posters.
Great Weapon Master: you're already resistant to most weapon attacks so might as well make reckless attacks for some sweet damage. CC is good but the best CC is a dead enemy.
Polearm Master: Your character will get access to Bonus Action: Attack. Barbarians arguably gets the most benefit from this one since they're not that much worst off with the lower AC from lack of shield and they get the minimum of +2 damage from rage.
Duelling: If taking a -5 accuracy for more damage is not your thing then Duelling for a straight +2 on top of your STR MOD and minimum of +2 from Rage might suit your play style more. At 20 STR you'll be adding + 9 on top of your damage die each hit. Try to get your hands on a longsword Flametoungue or similar items for stupid levels of damage.
If not taking Bear Totem Barbarian then consider taking the Gift of the Chromatic Dragon feat at some point. It allows you to do something with your bonus action, gives your attacks a little but of elemental damage while giving you resistance to an element at the cost of a reaction.
Flavor-wise: take the Tavern Brawler Feat, now you can use your enemies as your weapons after you grapple them
Ritual Caster: if your party is made up of all martial characaters
Skill Expert: if you want to add more prof bonus to your Athletics Grapple checks without dipping to other classes
Tough for more Tanky-ness
Sentinel is a Meh for Barbarian since you're better off selecting ASI to STR, DEX or CON
Resilient WIS: since being CC'd for half the fight is not fun.
Gonna give you something OTHER THAN GWM - a feat my barb9/fighter6 does not actually have. As someone else mentioned, if your focus is to maximize melee damage, a fighter is probably the better choice. Instead, my bard is more about taking damage (with awareness of the tank fallacy). I use a shield and trident.
One of my fave for my totem barb is Gift of the Chromatic Dragon. I get a low use (too many other BA options) 1d4 pick of elemental damage types but the main benefit is the 5 per day reactive resistance to elemental damage. This allows me to use my totem for Wolf to grant pact tactics to my party and still get the best features of bear totem.
Durable combined with Dwarven Fortitude is incredible. Tons of easy reliable hit points with just one quick dodge action.
DMing:
The Cataclysm Stadium
Rise of the White Mask
Optimization Guides:
Literally Too Angry to Die - A Guide to Optimizing a Barbarian.