There are a lot of different abilities in Apex Legends, and it's critical to keep all of them in mind when trying to gain the upper hand on the competition. These abilities can vary drastically in usefulness, but every ability does have a time and place in which it could be the difference between winning and losing.
There won't be room to describe exactly what each ability does and explain why it is/isn't useful, so here's a useful resource explaining what each character's abilities are.
26 MIRAGE: ENCORE
One of the least useful abilities in the game is, without a doubt, Mirage's passive ability. This trick works on someone approximately once, and they're forever wise to the bamboozle attempt in the future.
25 MIRAGE: VANISHING ACT
Mirage isn't useless, seriously! It's just that, well, only one of his abilities is really all that great. This ultimate ability keeps you from firing your gun, picking up a teammates banner, and really doing anything at all other than running.
24 WRAITH: DIMENSIONAL RIFT
While this ability (when used perfectly) can be a huge benefit, most of the time it's just not going to go as planned. It's too easy for opponents to trap one end of the portal with a Gas Canister, Jump Pad, or a firing squad.
23 BANGALORE: DOUBLE TIME
While this ability can get you out of trouble with a serious quickness, it's also no guarantee that it's going to help you avoid any bullets whatsoever.
It makes you a bit harder to hit, sure, but anyone with decent aim isn't going to have any problem keeping up.
22 OCTANE: STIM
Very similar to Bangalore's Double Time, Octane's Stim can be a useful tool for moving around quicker, but it can also end up making absolutely no difference. But, it can at least be activated on command!
21 GIBRALTAR: GUN SHIELD
This shield can make a life-saving difference in a gunfight, but it can also get you spotted by enemies if you don't pull it down in sneakier circumstances. Use it wisely.
20 PATHFINDER: GRAPPLING HOOK
In skilled hands, the grappling hook can be stupendously useful in getting on top of enemies before they expect it, or getting to spots that catch them off-guard. That being said, it's very situational.
19 CAUSTIC: NOX GAS GRENADE
This ability is a pretty good way to flush enemies out of a building or out from behind cover, but it lags a bit behind in the Gas Canister in terms of defensive capabilities. This can be a great tool, just make sure it's well-placed, and make sure it isn't going to end up obscuring a teammates vision.
18 WRAITH: INTO THE VOID
While Into the Void can help to get out of immediate danger, it does nothing to conceal Wraith visually. If she can't get into cover before the ability is up, all it's done is simply given enemies time to reload and regroup for a better shot.
17 BLOODHOUND: EYE OF THE ALLFATHER
This ability is certainly useful when it comes to figuring out exactly who your enemies are and where they're hiding. But, it gives away the Bloodhound just as much as it does anybody that gets scanned. Try to only use it if the squad's cover has already been blown.
16 WRAITH: VOICES FROM THE VOID
This can help avoid an ambush or warn you of approaching enemies, but a well-coordinated team is going to notice the Wraith and purposefully not aim directly at her until they're ready to attack. This can be a useful tool, just don't put too much stock in it.
15 LIFELINE: COMBAT MEDIC
This ability has more than one thing going for it. The quicker healing is nothing but helpful, cutting out those extra half-seconds that can make all of the difference. The revive shield can be nice, but it can also give away her position, too.
14 OCTANE: LAUNCH PAD
The Launch Pad can make all of the difference for a squad, but it can also benefit enemies every bit as much as teammates. If the Launch Pad is well-placed, it can often be a deciding factor in a fight, especially in a small circle.
13 BLOODHOUND: BEAST OF THE HUNT
Beast of the Hunt is one of those abilities that can only be as good as the player using it. That sounds weird (isn't every ability?), but this ultimate requires good gun skill, positioning, and decision making to be useful whatsoever.
12 PATHFINDER: ZIPLINE GUN
The Zipline Gun can be a crucial tool in getting the squad into a comfortable position in the circle, but it's very difficult to use without being incredibly visible. More often than not, using it is going to get you spotted, especially in a late circle.
11 BLOODHOUND: TRACKER
The ability to see enemy footsteps is useful enough, but the fact this ability enables you to see how long ago they were made makes it a super-useful tool. This can track more than just footsteps too; a good Bloodhound has a lot of information at their fingertips.
10 OCTANE: SWIFT MEND
The ability to passively heal ensures that it's mostly pointless to carry around stimpacks at all.
Medkits are still useful, but as long as Octane has a minute to recuperate after a fight, he should be around full health.
9 GIBRALTAR: DOME OF PROTECTION
This dome-shield can be a squad-saver, especially if there's an ultimate ability raining down from the sky. It can buy some time to revive a teammate, force enemies into a close-range fight, or just be some cover in an area without much of it.
8 BANGALORE: SMOKE LAUNCHER
Smoke grenades are incredibly powerful in just about any game that includes them, and that remains the case here. These can force enemies closer, allow someone to revive squadmates, bait enemies into wasting their throwables, or get the squad to safety.
7 GIBRALTAR: DEFENSIVE BOMBARDMENT
This ultimate is a beautiful, multi-purpose tool. Need to finish off a downed enemy that's behind cover? Need to force an entire squad out of cover? Or maybe pack them all into a building? This ultimate can do all of that.
6 BANGALORE: ROLLING THUNDER
Very similar to Gibraltar's ultimate, this one gains the advantage because of the "shell-shock" effect it gives. Enemies hit by this move and turn slower, making them super-easy to finish. Just be careful: the shell-shock effect can hit teammates, as well.
5 CAUSTIC: NOX VISION/GAS CANISTER
These abilities have to be in the same conversation because one essentially activates the other. Gas Canister can be placed around a corner to surprise an unsuspecting foe, they can be used to block a doorway, or they can just be set up as perimeter alarms. Once in the gas, Caustic is able to see through it without much impairment.
4 MIRAGE: PSYCHE OUT
This ability is why Mirage, despite having a couple of pretty terrible abilities, is still a super-useful character. This decoy is one of the most useful tools at any character's disposal, making it possible to point enemies in the wrong direction, get information on their location, and waste their time, among other things.
3 PATHFINDER: INSIDE KNOWLEDGE
Circle-play is key to winning a battle-royale. Knowing where the next circle is going to end up allows Pathfinder's squad to get an advantageous position before anybody else (hopefully).
2 LIFELINE: CARE PACKAGE
Gear is another pretty obvious key to winning in Apex, and Lifeline's Care Packages can give your team the upper-hand in that department. Keep feeding Lifeline Ultimate Accelerants, and her squad is probably going to entirely equipped with purple armor.
1 LIFELINE: D.O.C. HEAL DRONE
There's a reason Lifeline seems to be the most-picked character in the game. Her D.O.C. drone can heal all three teammates at the same time, and heal them a massive amount, too.