Dragon Age: Origins

S Tier (The Unkillable Juggernaut and the Healer)
Alistair: Increase his Strength by 2 and Dexterity by 1 every level, give him the best possible armour, as well as as many defense-enhancing rings and belts and shit as possible and boom, now you have an unkillable tank.
Wynne: Literally your only healer.

A Tier (Extremely Strong)
Morrigan: Probably the only reason she isn't in S Tier is because she doesn't really have that much healing capabilities. Sure, she can heal, but she's more of a high-damage caster than anything.
Leliana: Easily the best buffer and debuffer in the game with the Bard specialisation. Combine this with Assassin and you have an extremely strong archer held back only by low health and poor Strength.
Sten: Max out his Strength and you have a two-handed beast who can double as a tank if Alistair leaves your party or dies.

B Tier (Dwarf Tier)
Shale: Highest base health and ridiculous Constitution with unique weapons that solely rely on Constitution isn't as good as it sounds on paper. Still strong though.
Oghren: Enters combat, gets cocky, dies. Unless you've saved good armour for him, he's kinda useless.

C Tier (Rest in Peace)
Zevran: A Rogue who can't pick locks or do high damage without dying? I say this from experience because he died constantly during Nature of the Beast and used up all my Injury Kits.
Dog: Extremely limited as a companion. Sorry. That's the truth.

Dragon Age II

S Tier (Masters of Plot Armour)
Aveline: Oh, someone else is tanking? Unless it's you, you're fucked! In all seriousness though, Aveline tanks almost as good as Alistair.
Varric: The single most reliable companion in the franchise that isn't a tank or healer, and he's got a cool ass unique weapon. Just be sure to upgrade his crossbow.

A Tier (Mage Tier)
Anders: Literally your only reliable healer.
Merrill: Usually, you don't really want to rely on blood magic. Merrill, however, literally can't heal, and has to brute force her way through everything. Which means you kinda have to rely on blood magic.
Bethany: Leaves at the end of Act 1 (or immediately, if you're a mage), but while she's a party member she's one of your most reliable, especially if she's a healer. She comes back if she doesn't die.

B Tier (How Is This Possible)
Fenris: Kind of a downgraded Sten if Sten were an elf. The only thing Fenris has over Sten is his magic arm, and even then he's meant to kill shit, not tank. Can't even equip a shield.
Sebastian: Downgraded Leliana without the Bard specialisation. Just kinda mid. Also fucks off if you spare Anders in Act 3.

C Tier (The Other Rogues)
Tallis: Slightly upgraded Zevran but a temporary companion. Other than that she's pretty fuckin' useless.
Isabela: Her starting weapons are weaker than the weapons you should have at that point.

D Tier (Why Would You Let Him Tank?)
Carver. Just... Carver.

Dragon Age: Inquisition

S Tier (Two Completely Different People)
Blackwall: Oh, you thought Alistair was unkillable? As long as you have a healer (preferably Solas), Blackwall is literally immortal. Especially with Tresspasser upgrades.
Sera: Oh, another rogue in S Tier? Chaos archer with potion crap who can kill everything by using Tempest abilities because why the fuck not. Unreliable at times, but always extremely strong.

A Tier (Your Starting Companions... And This Bitch)
Solas: I was gonna put this guy in S Tier in favour of Sera, buuuut he's a mage and mages are generally a lot more versatile at the cost of specialisation. He's still a really strong all-around support though.
Cassandra: If Blackwall fucks off or gets executed, Cassandra's your best bet for a tank. Plus, Tresspasser upgrades are just kinda broken so everyone's busted anyway.
Varric: Slightly nerfed from DA2, you've still gotta upgrade Bianca constantly but overall he's still really strong. Artificer ultimately has more synergy with you but Varric can put it to good use too.
Vivienne: Holy shit, 2 mages in one tier again! A mage that can also tank... and Vivienne ultimately doesn't do that well at it, unfortunately. Still a good attacker.

B Tier (Just Barely Pre-Skyhold)
Dorian: You'd think the Tevinter, of all people, would be the best mage in the entire series that isn't a healer. Nope, this guy just temporarily raises people from the dead as a temporary bonus.
Cole: Zevran if he could actually do damage (and was also a spirit).

C Tier (Requires Significant Micromanagement)
Iron Bull: You'd think the Qunari, of all people, would be the strongest warrior in the entire series. Nope. He enters combat, gets cocky and dies pretty much immediately. We still love him though.

Ultimately I'd say the top three companions in the entire series, aside from Veilguard companions, are (from worst to best) Wynne, Alistair and Blackwall, and the bottom three would be (from best to worst) Iron Bull, Zevran and Carver (I'm not counting Dog because, come on, it's Dog).

This is subjective, feel free to disagree with me.