I see some people mentioned the Ability Hustle. Most Pokémon that have the Ability Hustle are not fully-evolved, meaning that you are unlikely to be using Hustle competitively anyway. The fully-evolved Pokémon that have Hustle are typically really weak and/or have better Abilities. Either way, in playthroughs, it isn't that bad, at least not to me. I don't mind trading some accuracy for more damage. Anyways, regarding my list:
Anticipation – The Pokémon shudders when the opponent knows a move that is super effective against it. This is pretty useless in my opinion because most players will be running vast coverage. Maybe this is better for in-game playthroughs, but even still, I don't know. I never really cared to know if any of my opponents knew a super-effective move, even in in-game playthroughs.
Arena Trap and Shadow Tag – In playthroughs, it is very annoying when I run into Diglett or Dugtrio with this Ability and I can't run or switch. It's pretty bad when you're EV training, as you're forced to KO the Pokémon, which may net the wrong EVs to a certain Pokémon. In competitive, it is just very annoying and cheap, as players can pull shenanigans with Choice items and Trick, effectively trapping you into endless battles. It's a very stupid Ability and really doesn't need to exist. Shadow Tag is pretty much the same thing but worse because, unlike Arena Trap, it works on all Pokémon instead of just grounded Pokémon.
Damp – Prevents the use of self-destructing moves such as Self-Destruct and Explosion. The only thing this really came in handy for was when I was Shiny hunting Forretress in Violet, which can explode. I used Golduck with Damp, which actually worked, thankfully because it sure did attempt to explode. Other than that, Pokémon don't typically explode during playthroughs and competitive players don't really explode like they used to since Explosion and Self-Destruct were nerfed since they no longer halve the target's Defense stat.
Defeatist – The signature Ability of the Archen line is pretty bad, as it halves the offensive stats when HP is dropped to half or less. While I understand that the developers likely gave this line the Defeatist Ability to balance Archeops' high base 140 Attack stat, by today's standards, it wouldn't even be broken because it's not unusual for Pokémon to be that powerful nowadays, and Archeops doesn't even learn many powerful attacks to truly take advantage of its high Attack stat. It can't even learn Head Smash or Brave Bird.
Forewarn – It reveals one of the opposing Pokémon's moves. Mainly, it reveals the move with the highest base power, but if more than one move have the highest base power, it would reveal one of those moves at random. If a Pokémon has only status moves, it would randomly reveal one of those moves as well. Similar to Anticipation, it just seems like a useless Ability because, personally, I don't need to know what move the opponent has, but I don't know; that's just me. In playthroughs, I feel I can deal with whatever I'm facing regardless. In competitive, I have enough experience to know what set my opponent is likely running anyway. Other players might feel differently though.
Honey Gather – I always thought the Honey system to attract wild Pokémon sucked in previous Pokémon games. To me, it was just another way of making catching Pokémon unnecessarily tedious. Now, Honey only serves the purpose of being sold to shops. To make matters worse, Honey sells for low prices. Thus, an Ability designed only to gather a cheap sell item is pretty bad in my opinion, even for a regular playthrough.
Klutz – Negates the effect of held items for the Pokémon with this Ability. The only thing this Ability is useful for is pulling Trick or Switcheroo shenanigans, but even still, much better Abilities exist.
Run Away – An Ability that guarantees the ability to flee from wild Pokémon despite use of trapping moves and trapping Abilities such as Arena Trap. It sounds good on paper, but for the most part, only really slow Pokémon are going to have trouble fleeing. Most of the Pokémon with this Ability are quite fast anyway. You're better off simply purchasing Pokédolls or Smoke Balls.
Shell Armor – Protects the Pokémon from critical hits. Maybe it is just me, but I always thought it was kind of pointless to protect a Pokémon from random RNG. Sure, critical hits can be a difference maker, but I don't think they're serious enough to warrant an entire Ability to protect a Pokémon for them. I believe Pokémon with this Ability can do so much better with other ones, with regular Unovan Samurott being the best example. Maybe it can come in handy against Pokémon that know moves that guarantee critical hits such as Meowscarada's Flower Trick and Urshifu's Wicked Blow or Surging Strikes, but that is situational.
Slow Start – Halves the Pokémon's Attack and Speed for five turns. This Ability is horrible and shouldn't exist. It was made to keep Regigigas from being overpowered, but it is a major legendary that is the leader of another legendary group, the Regis. For that reason alone, Regigigas should be extremely powerful from the start. It deserves so much better. Varoom even has this Ability as a Hidden Ability. I guess, similar to real life cars, some varoom just have trouble accelerating?
Stall – Although it is the signature Ability of Sableye, the Ability that forces a Pokémon to always go second is too much of a hinderance. Devalue mentioned how this is supposed to help power up Payback, but Sableye isn't exactly the best Pokémon at taking hits, especially in single battles.
Truant – Causes the Pokémon with this Ability to move every two turns. This Ability is horrible because Pokémon with this Ability can literally be completely stopped by Protect and similar protection moves. I would say that, next to Slow Start, this is arguably the worst Ability in Pokémon. This Ability was made strictly to keep Slacking from being overpowered, which makes sense because Slaking is an early-route Pokémon that is literally as strong as a major box legendary. My question is why is Slaking even that powerful to begin with? Another question is why does Durant have this as a Hidden Ability? Ants are supposed to be very hard workers in the insect world. Are some Durants just lazy?
These are all the worst Abilities that have come to mind to thus far that I have experienced in regular playthroughs and competitive play.