To be brief i'll just list the the ones that i remember the best.

NwN: Linu, Grimgnaw and Deekin [SoU],
NwN 2: Grobnar <span class="bold">and here is why</span>
DAO: Shale, Zevran, Leliana, Morrigan, Anders [DAA] and ser Gilmore [Companion mod]

HK-47 from KOTOR - Guess where my forum handle came from. :P
Elizabeth from BioShock Infinite - She's pretty much the best part of the game IMO.

I liked my horse companions, even more so if I can load them down with supplys, nothing like being able to sell junk when you get back to town.
Know that I think about it, there are no skyrim/oblivion mods, that require horses to be feed/watered/slept... are there?

I need a game where my partner (dog, horse, non-human) survival depends on me, that sounds like a nice game to me.

I also like HK-47 cause his personality! I still chose him over other partie members that happen to be better in combat.
Usually just me and my droids hanging out, that way the beer lasts longer!@

Torian Kel, here's why.

As much as I love Fallout. The NPC Companions had like almost zero personality, they annoyed me constantly always wanting to get shot in the back with friendly fire and were only good as pack mules =P ....Oh wait the dog, yeah the only likeable NPC, he was great, too bad he couldn't carry stuff and liked walking into deadly electric fields....

So yeah my vote for favorite and very useful NPC companion would definitely go to HK 47 from Star Wars: Knights of the Repubilic. It's among my top 5 fav console games I think, well it's way up there. It's a shame what happened with the MMO transformation of the series.......that a whole other can of worms tho.....=/

Dogmeat from Fallout.

Boo!

You mean Lydia who's always coughing, babbling or making weird noises at the most inappropriate times and who can turn a harmless tavern brawl into a massacre? :D

Imoen is definitely a good choice. I have to admit though, I'm a sucker for funny characters and the first memorable companions who come to mind for me are Deekin from the NWN expansions and Morte from PST. And speaking of PST, I also liked Annah a lot.

EDIT: Oh yeah, Edwin from BG 1&2 is one of my favorites, too.

For me, honestly, I'd say the rogues of Diablo II. I don't know. I mean they're helpful because of their bows and all. Plus they're probably hot IRL. LOL. Yeah, I guess that's it.

I deliberately did not mention the reasons why my relative chose Lydia because I was curious as to how people would react to that choice. So let me explain.

In his view Lydia is the perfect NPC companion because she's (a) a great pack mule (b) you can marry her (c) she runs your house for you and (d) she even opens a shop for you and gives you money. In his view, the perfect woman.

It's a different view on makes a good NPC character and a reminder that not everyone judges people by the same standard.

Liara from Mass Effect. Silken voice, good looks, very helpful biotic power singularity.

I don't play many games with NPC Companions, but I have to say after playing "Beneath a Steel Sky" recently I really liked Joey the robot. He's annoying (as I find all NPC Companions), but in a very funny way :D!

It's not even close for me. It's HK-47 from KOTOR 1!

Eleanor - Bioshock 2

Veronica and Cass from New Vegas immediately sprang to mind. Very different female characters who are both awesome. "Whatever the size of Caesar's pecker, he's sure giving the Mojave a good fucking."