Greetings!
So this is a thread intended primarily for folks to share their own rankings of the feats and their reasons for doing so. I'll share my rankings, but I would absolutely love it if instead of just critiquing what I've got folks share their own lists. I think we'll get more useful information for folks and have this be a more useful thread if folks do. Without further ado, I'll kick it off!
S Tier:
Tavern Brawler - Utterly broken. An ASI is incredible for adding +1 to hit and +1 damage (among other bonuses, but those are typically the most important). To instead add up to +8 to hit and +8 damage? Ridiculous. This is a large part of why Monks are as absurdly good as they are, and the fact that it gives +1 Str or Con on top of its effects is just silly.
Lucky - This would be lower, much lower, if you needed to decide whether or not it was being used before the result of the die was revealed. As is, getting a reaction to make it so an enemy does not in fact crit when they would have, or that someone does not miss that crucial attack or skill check or saving throw, *after* it has been determined that something bad has happened, is just amazingly good. The fact that you get to apply it not just to yourself but anyone you can see, is ridiculous.
Elemental Adept - Ignoring resistance and allowing you to use your themed damage type with something like a Storm Sorc or Tempest Cleric or whatever enables the efficacy of a build in a way that other feats just don't do. It's doubling your damage when it applies. Sure, it won't always apply, and not all builds need it. But if you're running a themed damage build it's the obvious must have choice, thus S tier.
A Tier:
Polearm Master - The bonus action attack is nice, even if it is bugged making it far less nice than it should be. But the real reason this is so nice is due to the reaction attack when a target comes into range. In practice, this can double the number of attacks a character has at level 4, and it remains useful throughout the game. Obviously it's not useful if you're not using polearms, but for anyone who even has them as an option it's quite potent.
Sentinel - Getting additional attacks via feats is always going to be very, very powerful. The reaction attack is somewhat uncontrollable but triggers more often than you might think. The denial of movement is quite nice as well, and it has strong synergy with say Polearm master which can outright prevent enemies from getting into melee range, leaving them stuck within your range but outside theirs, which is a great time.
Great Weapon Master - It grants a toggleable mode switching between damage and accuracy. If you have a reliable source of advantage, in the early game it can be a 50%+ boost to damage output. The Bonus Attack remains useful in all situations and throughout the game.
Sharpshooter - +2 to hit when attacking high ground foes in and of itself is nice. The toggleable mode switching between accuracy and damage is incredible, same as Great Weapon Master. Can be a +50% damage increase or more, you need to see it in action to fully appreciate it.
Actor - Grants a Cha increase and proficiency *and expertise* in 2 skills which are very useful for your Cha based character. So much better than skilled it's ridiculous, and Skilled is already a good feat.
Athlete - The reduced movement cost for standing up prone is somewhat useless. +1 Str or Dex is ok. The 50% increase in jump distance is very good, and can allow you to bypass difficult terrain and reach areas you otherwise could not, significantly increasing the mobility of melee and ranged characters alike.
Warcaster - The reaction shocking grasp is ok but not amazing, but advantage on maintaining concentration *is* amazing. Concentration based spells are some of the most powerful in the game, and maintaining them reliably is very potent, in terms of saving spell slots and resources and ensuring debuffs stick.
B Tier:
Heavy Armour Master - It would be a tier higher if it was all damage and not just non-magical attack damage. It's nice, as with certain sets of Heavy Armor you can get -5 to incoming non-magical attack damage, halved if you've got Blade Ward or Rage going. This makes you *very* tanky. But spells and magical attacks ignoring it completely reduce its effectiveness, and its usefulness is reliant on the idea you're taking a lot of incoming hits, so it gets worse the better you get at the game and the easier you can kill your enemies. Still good, just not amazing.
Magic Initiate: Druid - Guidance and Resistance are two of the best Cantrips. Druid has several great 1st level spells including Speak with Animals, Enhance Leap, or Faerie Fire. Very good overall.
Mobile - If you're a melee character, mobility is king. You deal 0 damage while at greater than melee range (generally), so +3m base movement speed, which then gets enhanced further with move speed bonuses, as well as universally ignoring difficult terrain, is quite good. Jumping is often better than running which is why this isn't higher.
Moderately Armored - Rogues specifically can make great use of this, as there are several sets of medium armor which are exceptional for high dex characters, and they can use the +1 Dex to even out an odd starting score. Most other characters don't even have it available to them, so the percentage of time where it's useful is higher than one might expect, and the benefit it can provide is quite substantial, up to +4 to AC.
Skilled - Skill proficiencies are quite good, 3 is a large number of proficiencies, and being able to choose *any* skill you want lets you completely round out the skills for a given attribute rather easily. While it doesn't impact your combat efficacy, skills are often pass / fail checks without redo opportunities, and passing them more consistently is fantastic from a RP and overall game experience standpoint.
Spell Sniper - +1 crit range on spells, which stacks, is very nice. The bonus damage cantrip is ok but not amazing. Overall it's a good, very solid feat choice which can do well in certain builds.
Dual Wielder - It's not for everyone, but it can let you do some silly things, like dual wielding staves for higher spell save DC bonuses and other unusual build options. Though those builds are unlikely to be particularly overpowered, nonetheless they are only possible with this feat, thus it's as high as it is.
Alert - Going first is very useful for alpha striking enemies, and especially if you have a class feature which lets you leverage that, like Assassins do. An inability to be surprised is also quite nice.
Heavily Armored - This can be nice for certain builds, letting them full dump Dex. Though you can get this with a dip in a class, there are situations where the feat is preferable.
C Tier:
Mage Slayer - It's actually quite good, when it applies. You break concentration easily, you get extra attacks against mages, and advantage on saves against them. It's just all very situational - how often is the character in question adjacent to a mage maintaining concentration on something in the first place? How often do they just cast something on you while in your face instead of trying to walk away first? If it wasn't so reliant on situations which you can't necessarily force (And wouldn't typically want to), it would be much higher. As is, it's here.
Magic Initiate: Anything Else - None of the other classes have as good of a spell list for Magic Initiate specifically. Eldritch Blast isn't amazing without its invocations, and while there are certainly options and you can certainly add value with this feat, generally speaking you're not getting anything you can't get from other sources (such as scrolls) which will actually significantly change your game experience or effectiveness.
Defensive Duelist - It can be quite nice, +4 to AC, and ways to increase your utilization of your reaction are always appreciated. But it doesn't give it for the rest of the turn like the Shield spell does, just for that one attack, and the triggering attack must be melee, both of which limit its usefulness.
Shield Master - Same as above, the utilization of a reaction is great, and taking no damage on the successful save is great. But the scenarios where it applies are limited, and entirely outside of your control. It must be a dex save, and it must have been caused by a spell. This limits its usefulness.
Savage Attacker - It's generally +1 to +3 damage, often around +2 damage. It's nice and feels even nicer, but it's hardly going to be a game changer. Additional damage and more consistent damage is never a bad thing.
Dungeon Delver - It has a host of benefits - resistance to damage, advantage on perception, and advantage on saving throws are all quite nice, and traps are quite plentiful in the game. However the narrow range of it, just applying specifically to traps, means it's of limited effectiveness.
Ritual Caster - Unlike PnP 5E, where you get *all* ritual spells for a class, this gives you only 2, which you must pre-select at the time you choose this. All of which have plenty of other ways to obtain them, and as they're ritual spells, if someone *does* have them from another source they're not using spell slots to cast them. As such you're not gaining anything from a resource efficacy standpoint. All of the choices are decent things to have available to you (speak with dead, speak with animals from a RP standpoint, familiars are always nice, Enhance Jump is great, and Disguise Self has some buggy interactions you can exploit) which saves it from falling further.
D Tier:
Resilient - The trouble is, anyone who would want this as a half feat likely can't take it, as they're already proficient in their primary ability's saving throws. About the only case where someone may want to pick up an extra proficiency would be Wizards or other spellcasters grabbing Con proficiency to maintain concentration, and in that case it's strictly worse than Warcaster granting advantage on them. Tough to ever justify.
Martial Adept - Battle Master Maneuvers suffer from needing to pass 2 checks for them to apply an effect - you need to hit *and* for them to fail their save, generally. Getting 2 maneuvers and 1 superiority die per short rest just isn't going to actually do much for you. For a battlemaster this is *slightly* better but that's just one subclass of one class, and not enough to change the overall ranking.
Performer - As hilarious as it may be to have your entire party take this feat and throw impromptu concerts everywhere you go, it's pretty much useless. You can get this for free on a character if you care about it and aren't running a bard, and otherwise the most you'll get on this is a couple of gold every now and again. Only the fact that it's fun from an RP standpoint saves it from F tier.
Tough - +2 HP per level is nice, but not that nice. It's tough to recommend.
Weapon Master - The +1 Str or Dex is a nice bonus, but generally there are better ways to gain proficiency in a specific weapon classification than via a Feat. It's tough to envision a scenario where a character would both desperately want a weapon proficiency they don't have to enable a build, and also doesn't have a better option for how they would obtain it.
Crossbow Expert - Avoiding disadvantage at point blank range is nice, but rarely is it the optimal play. Additional Gaping Wounds duration is utterly useless. Overall it feels like a mistake for someone to take this, *even if* they're focused on a ranged crossbow build, but it's not entirely and completely useless, landing it in D tier.
Charger - I honestly haven't tested this, it may be better than it looks, but it looks aweful. From an action economy standpoint it doesn't really seem like it's doing much other than maybe sometimes effectively giving you a bonus action attack you wouldn't otherwise have had if you would've been dashing, or a free bonus action shove. Both of which are predicated on the idea you're using a full action dash in the first place, which is something best avoided whenever possible. Is that worth a feat? It's hard to see how it would be.
F Tier:
Lightly Armoured - May well be the worst feat in the game. Only Monks, Wizards, and Sorcerers (or a MC combo of those) are even eligible for it. Setting aside the idea that generally they don't want or need it (they have as good or better options among clothing than they would light armor), it would only take a 1 level dip in Ranger to get Heavy Armor Proficiency, which otherwise would take 3 feats to achieve, with this being only the first of them. Wildly useless.
Medium Armor Master - For someone who wants to use Medium Armor, who needs more than 2 Dex bonus applied, and doesn't want disadvantage on stealth, there are armors available which already have those effects built in. The use case for this is just so incredibly narrow.
Durable - Getting all your HP back on a short rest is just not useful. Any situation where you can take a short rest you can also drink some of your plentiful healing potions, you often will short rest without being significantly more than half dead in the first place, and having one character full heal while the rest don't isn't strategically advantageous. It's very likely to be totally useless to you.