So, the way combos in ME 2 work is that they have two components, a primer, and a detonator.
Whenever a target currently affected by a primer is hit by an eligible detonator, there's a chance that explosion occurs based on the specific combination of effects in play. For example, Biotic Charge is capable of detonating all four varieties of combos. If a target is hit by Warp first, which acts as a primer, a Biotic Combo will trigger, which explode in an area effect for decent damage against health, barriers and armor. Biotic Combos are also notable in that they are the only Combo that triggers 100% reliably, regardless of the health of the target. Others may require a killing blow, or a fair amount of luck.
If instead of charging a target affected by warp, we had charged a target that had been set on fire by Incendiary Ammo, we'd have a chance of triggering a Flame Explosion, which will set victims on fire, causing organics to panic.
There's a whole variety of combinations that can produce one of four types of combos (Biotic, Flame, Electric, Cryo), so experiment!
With regard to the various Detonation upgrades, they specifically effect combos detonated by that power. As a result, they are incapable of stacking.
There's technically three types of powers in Mass Effect: Active Powers, Grenades and Passive Abilities.
Active powers a single Global Cooldown. A skill either activates the Global Cooldown or it doesn't. Skills that don't activate a cooldown are only limited by how quickly you can perform the action (the time it takes to switch ammo/throw a grenade).
Most powers listed as a base power here qualify as Active. These are your standard attacks and always cause a cooldown.
Passive powers are always active and don't have cooldowns, simple enough. Ammo powers are technically passive, and you can always switch ammo regardless of cooldown. Tech Armor is basically a passive power unless you detonate it.
Grenades don't use a cooldown either, and if something seems like an "active" power and it doesn't activate the cooldown, that's because it's technically a grenade. Proximity mines, Nova and Sentry Turrets are all technically grenades.
Nova has a "cooldown" that's actually based on your Biotic Barrier (the purple "shield" Vanguards have). You can't use Nova if your Biotic Barrier is empty, but it otherwise ignores cooldowns like a grenade.
Best Answer
I found this list of biotic and tech combos on the Bioware forums.
Biotic Combos
Singularity --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Stasis --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Pull --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Warp --> Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Lift Grenade --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade, Reave
Shockwave (only with Rank 6 Lifting Shockwave evolution) --> Warp, Throw, Charge, Nova, Cluster Grenade, Reave
Reave --> Warp, Throw, Shockwave, Charge, Nova, Cluster Grenade
Tech Combos
FIRE EXPLOSION - Can be set up by: Incinerate, Carnage, Inferno Grenade, Incendiary Ammo
Can be detonated with any Biotic/Tech/Combat powers that can deal direct damage (except for the powers that are used to set up the combo).
Effect: Enemies effected by any of the fire based powers, cause an AoE fire explosion, once they are killed by a direct damage power. The effect is similar to blowing up Pyros with Overload in ME2.
Note: Enemy MUST be killed by the second power, in order to cause a Fire Explosion. E.G. it will not work, if an enemy is hit by Incinerate --> Overload, and still has HP left after that. So, in this case, Overload would have to do sufficient damage to outright kill a burning enemy, in order to cause a Fire Explosion.
CRYO EXPLOSION - Can be set up by: Cryo Blast, Cryo Ammo
Can be detonated with any Biotic/Tech/Combat powers that can deal direct damage.
Effect: Frozen enemies killed by damage based powers, cause an AoE cryo explosion, freezing any enemy that is nearby.
Note: Same as Fire Explosion, frozen enemies MUST be killed by the second power in order to trigger Cryo Explosion.
TECH BURST - Can be set up by: Overload, Energy Drain, Disruptor Ammo, Sabotage
Can be detonated by any Biotic/Tech/Combat powers that can deal direct damage (except for the powers that are used to set up the combo).
Effect: Enemies effected by electricity based powers, discharge multiple electricity bolts to nearby enemies, when hit with direct damage powers. Effect is similar to Overload's Chain Overload upgrade.
Note: Unlike Fire & Cryo Explosion combos, this one doesn't require an enemy to be killed by the second power. E.G. enemy hit by Overload --> Incinerate will produce Tech Burst, whether he is killed by Incinerate or not.