I don't play Zaalbar the Wookie (weak defense) or T3-M4 (well...) but almost everyone else has found a place in my party at some point

I like Bastilla, naturally, Canderous, Jolee.
My most-often used combo (with a soldier-type character) is probably Bastilla/Jolee and later Juhani/Jolee. Three Jedi are, as has been pointed out many times,
unstoppable 
An upgraded HK-47 or Canderous sometimes make it in with good ranged weapons, but in the games I've played so far, I've mostly stuck with Jedi.
Funniest/coolest NPC? I have to agree with fable here, HK-47 is nothing short of hilarious.
Bioware have set up the NPCs in a very convenient way ~~ they all gain experience as you progress (so in fact you have no disadvantages for leaving someone behind except for not having them in battle or not activating side quests), you have unified inventory system, etc.
Cheers,
-katsuburi
~~ aim low, deliver.