Human Engineer + Executioner: I have posted about it many times here, awesome fun, and it actually makes good use of Power Efficiency Mods!
Salarian Infiltrator + Crusader - Drill Ammo: Max power damage so you can 1-shot enemy shields with Energy Drain, makes taking down mooks a snap. Also Proxy Mine + Drill Ammo means that bosses melt, especially any boss that can be multi-hit. You can almost take out a Gold Ravager with a Proxy Mine + single Crusader shot.
Geth Engineer + Phaeston + Incendiary Ammo: Actually makes the Phaeston fun. Spam Overload as much as possible and fire steadily in between. Definitely use Flamer Turret for extra fire explosions and for distracting enemies.
Geth Engineer + Valkyrie + AP Ammo: Headshot machine. Hunter mode's accuracy boost makes double-tap headshots very possible. Just remember to ADS. Also use Flamer Turret for this one.
Human Infiltrator + CSR + Incendiary Ammo: Cryo Blast debuff plus CSR's insane DPS melts bosses but good. Cryo Blast is good for forcing a stagger or dodge, making it easier to take out mooks too.
Asari Adept + Disciple + Phasic Ammo: Strip shields without having to carry the Acolyte, and look/sound cool when you do it. Disciple stagger also provides easy targets for Warp, which makes Warp-Throw combos on mooks a viable killing strategy.