Drell Adept:
Nuke 'em.
Quick hit and run tactics. Pop out of soft cover, cast reave, throw grenades, enjoy killstreak. Evading straight up fights for bombing runs on hard pockets or boss enemies.
Asari Justicar:
Fortress.
Just a straight up defensive bulwark. When alone this build confines itself to reaving and then shooting everything on sight, preferably from inside the defensive bubble. When other biotics are in the team, I play the BE primer.
N7 Fury:
CQC BE Bomber.
Activate AF, run into mobs, Throw, revel in bluesplosions. That's basially it. Exploiting the melee DR here and there. Very agressive build.
Turian Soldier:
Hold the line playstyle.
Move to position and unleash an unending barrage of death on the enemies. Move to another position when deemed necessary or profitable. Will get agressive and start hunting down individual enemies at the end of the wave.
Batarian Soldier:
In-yo-face playstyle.
Graal Spike Thrower, Exploding Ballistic Blades, Blade Armor, whatever, this soldier is the epitone of spike'y. Very aggresive build. Run up onto the enemy, BB+Graal for stagger, then heavy melee Falcon Punch in the face. Rince and repeat until everything got its head smashed into a fine red slur. Will need some medic attention most of the time but hell if I didn't out balance that inconvinience by thinning enemy hordes considerably.
N7 Destroyer:
Master at arms.
Just straight up un and gun, terminator mode. Relentless onslaught of whatever crosses my front, my Destroyer is very much akin to the crawling barrage. Aggressive of course.
Salarian Engineer:
Deception.
Decoy is the go-to power. Strategically pop a Decoy, then ED and incinerate everything that's enthralled by its shiny. Rince and repeat. Can do defensive, manouvre and even limited aggressive playstyles.
Demolisher:
Grenades, duh.
Straight up nuker. Get a corner, set up Pylon, throw grenades, wait for grenade refill, then move up to another position if needed. A rather defesive playstyle.
Krogan Sentinel:
Brawler.
Your standard Krogan melee built. Falcon for AoE stagger, then either Liftgrenade or heavy melee, mostly heavy melee. Very aggressive.
N7 Paladin:
Brawler.
Another CQC+Melee built, though not confined to that role. Points in ED and SF make it good for anti shield/barrier casting and short range power damage. Will liberally run up onto enemies, bash them with the flameshield and then SF for a FE. The occasional aggro manager with the shield to take the heat of teammates. Mostly played aggressively.
Salarian Infiltrator:
Valiant/Blackwidow sniper.
Your standard Salarian Infiltrator sniper built. A rather defensive playstyle.
Geth Infiltrator:
Javelin sniper.
Maximum damage single shot sniper built. Very defensive due to the limited GI health/shields.
Male Quarian Infiltrator:
Burst damage with Claymore.
Claymore Infiltrator (damage) with grenades and stuff. Typical burst dps CQC built. Aggressive playstyle.
N7 Shadow:
Hack'n'Slash.
Duration Infiltrator built for maximum melee damage and SS. No ES. Runs on constant backstabbing. Very aggressive.
Novaguard:
Novaguard, duh.
Straight up Novaguard gameplay, obviously very, very aggresive.
Asari Vanguard:
Stasis Vanguard.
Vanguard+Eviscerator/Wraith+Vulnerability Stasis=Win. Moderately aggressive, mobile CQC built.
I think that's all of them.