for sure:
assassin's devil's cough (10/15/20, loading) opt
assault's HIR HAR (10/12/14 AP loading) opt
operator's plasma rifle (7x1/2/3 attacks, +2 accuracy, just nuts)
pyro's napalm bomb (aoe 2/4/6 heat and 3/4/5 burn, loading) opt
ronin's sword (high damage 6x1/2/3 and 1d6 crits and accuracy)
specter's sword (crazy damage against lone targets, though the specter has to not be hidden)

really likely:
hornet's hex missiles (aoe heat is cool) opt
pyro's flamethrower (cause it more heat, burn is pretty high too)
rainmaker's missile pods (decent arcing reliable 2/3/3 damage 4/5/6 on up to 3 targets and knockback 1)
scourer's thermal lance (4 self heat and mediocre damage. possibly big damage next round)
scout's marker rifle (pretty damn useful)
sentinal's shotgun with wrath-lock (makes the damage worthwhile and it's good to waste)
berserker's aggression (attack them to waste it and get more damage)
berserker's retribution (combines with the above and waste it's damage) opt

maybe (and I really mean _maybe_):
ace missile launcher
archer's LMG
assassin's heated blade
assault's grenade launcher opt
bastion's grenade launcher
berserker's chain axe
berserker's harpoon cannon opt
breacher's shotguns (only great against demolisher)
goliath's retribution opt
hive's nexus (burn is kinda cool?)
hive's seeker cloud (aoe lock-on is cool) opt
operator's nova missile (it's seeking aoe, maybe) opt
ronin's echo edge (it has control when the marks trigger) opt
scourer's pulse laser (it's line 10, and can fire twice at t2-3) opt
seeder's grenade launcher (the damage sucks 2/3/4, knockback 1)

almost never:
barricade graviton lance
assault combat knife
bastion's heavy assault shield
berserker's nail gun opt
breacher's flechette shot opt
cataphract ram cannon (damage is meh)
engineer's flak cannon (depends on your mech)
goliath drum shotgun (worse breacher's shotugn)
hornet's stinger pistol (just invade)
ronin's rebound (why would they ever use it?)
sentinal's weapons (damage sucks on both)
specter's machine pistol (damage sucks) opt

can't:
bombard cannon
demolisher hammer
sniper's rifle

no weapons:
mirage
priest
support
witch