Companions you NEVER use

Juggernaut:
Lt. Pierce
Broonmark (heck I keep forgetting Broonmark exists, he's my non-existant companion)

Operative:
Lokin (I vendored his gear within 40 seconds of getting him, an Operative doesn't need a healer companion)
Scorpio (I had Kaliyo geared, why bother with Scorpio since droids are a pain to gear?)

Mercenary:
Skadge (I don't like him and I didn't bother getting him geared)

Trooper- Yuun:
You just get him so late and its a bit hard to form a connection to him because...... well hes a bug.

Jedi Knight-
R2D2: I just really though Kira was awesome even though she was clearly worse in practical terms as a companion for my sentinel so I overlooked R2 after the very early game.

Sergeant Rusk: You get him so late and the JK just has much cooler options than Rusk.

I have played most companions at least a little to get a feel for them. However, I don'r recall ever using Sgt Rusk on my knight or Akaavi Spar on my smuggler.

SW....I never used Broonmark, Pierce.

SI...I never used Talos, Xalek or Ashara

IA...I never used Lokin, Temple or Scorpio

BH...I never used Skadge, don't like Mako and got tired real quick of Torian.

JK...never used Rusk or Kira

JC...not far in enough yet...

Trooper...hate all of them. Arik annoys me the least. Elara...just march that bish out and shoot her plz.

Smug...never used Akavi, Risha or Gus.

Hmmm lets have a look...

SW - Broomark, Pierce, Jaesa (I regret picking her as dark side, she is an utter psycho)
Trooper - Everyone but Jorge (levelled as a healer with a friend)
JC - Iresso,
JK - Doc (levelled as tank with a healer friend ), Rusk, Scourge

Kaliyo because she is psychotic.

All the companions will work though. If you want some challenge leave your healers tucked away as they are OP compared to the other comps. Tharan is a monster with his stun.

For me, It is always what you are dictates what you wont ever use, eg, as a tank you will never use a tank companion and so forth.
My least used/not used:

Trooper: Yuun/Tanno Vik
Smuggler: Bowdaar/Risha
JK: Fideltin Rusk/Lord Scourge
Consular: Tharan Cedrax/Zenith/Felix Iresso
Bounty Hunter: Skadge/Gault Rennow
Warrior: Vette/Lieutenant Pierce/Broonmark
Inquisitor: Andronikos Revel
Agent: Doctor Eckard Lokin/Raina Temple/Scorpio

The robot companions in both factions (not including HK-51)

I never use droids , I always send them to missions.
I never use companions other then tanks at leveling. Tanks are fastest for leveling because

Healer companions lack damage
Damage companions deals best damage but its not as much as to make a big difference and they die too fast on elites.

Tanks are best because they keep agro absorb lots of damage contribute to my dps with their little damage. I never heal them or resurrect them after the fights. I dismissed them and resummon so they come with full hp and their debuffs cleared in 1.5 seconds.

I use healer companion for world pvp and any other activities.

For my warrior, Pierce and Broonmark. For my trooper, Aric is just annoying. Once I get another companion I won't be using the knight's droid as I hate how they talk (who thought that would be a good idea?).