I guess I'll have to play KotOR after all ...

KOTOR is like Dragon Age in that regard.

Right away my mind goes to the KotORs and PS:T. Sort of thinking of Arcanum too, though they can also be frustrating. Remember their quips from The Dark Eye: Drakensang too, but discussions don't advance and annoying with how they reposition in combat. Also something interesting in Septerra Core, though mostly I remember how some hate each other and will attack each other in combat until you manage to make them sort out their differences.
Then, looking through what I played. They are interesting in Anachronox. Maybe a bit to be said about NWN: HotU too. In Betrayal at Krondor, being a story like it is, they feel more like actual companions than... helpers, if you will. Something to be said for VtM: Redemption too.

I usually don't like companions in games, I find them a nuisance, but I like the pets in Torchlight.

I absolutely loved Shale in Dragon Age. Not only is she a fun addition to the party combat-wise, but her background and dialog are some of the most memorable things in Dragon Age for me.

Whenever I play Ocarina of Time I'm suddenly cured of any attachment to my companions, so I don't think I can answer this question.

HEY!

LISTEN!

HEY!

Incredible Adventures of Van Helsing games have a pretty useful companion.
Acts as melee-tank or ranged fire support depending on the skill loadout, does the "auto-sell unwanted/old/crap gear to town vendors" stuff, and is also the plot exposition/primary snarky humor source of the game.

Elder Scroll Games with modded hentai waifus

Breath of the Wild: Your companions are great power ups and you actually have to earn them.

Dragon Age: Origins

AI-wise:
You can script your character and companions to do things like:

Drink potions at a certain threshold.
Determine who to attack (dependent on enemy tier, health, current health etc.)
When to use certain abilities.

and many more things.

I never used it because manual control will always be superior and I used pause to direct tough fights action by action for each party member.

Still, a very nice feature which most games lack.

And when it comes to tweaking their kits, you can level every party member separately by distributing attribute points, skill points and choosing their specializations.

Too bad the RPG aspect took a nose dive down a cliff in Dragon Age 2 and Inquisition compared to the original.

When it comes to cRPGs:

Baldur's Gate I/II
Planescape: Torment
Mass Effect 1/2
Shadowrun Returns/Dragonfall/Hong Kong
Dragon Age: Origins

You poor, tortured soul. What abominable, hellish pits of despair must you have been dragged through, to find solace in such unfathomable depths of madness.

You have my deepest sympathies. Only one.

The princess in Prince of Persia: Sands of Time isn't TOO annoying & a crack is never far away. Sweet, blissful silence...

Seconded, really good game.

Independence War 2: Edge of Chaos. They do their jobs really well but not inhumanly so. Some of them are funny. I attached conversation pictures with two of them, one ex-human and one living human.