Diablo – Do followers trigger traps

Unlike in Diablo II, on-hit elemental damage is simply that - bonus damage, with the sole exception of cold damage (which has a small snare). Frost damage does a little less damage comparatively because of this.

While there was originally a more complex critical hit system (as documented below), that functionality did not make it to the final game.

Critical hits just add damage.

Historical Answer:

More interestingly, in the Diablo III Beta, each type of damage has a different effect on a critical.

• Physical: Double Damage

• Arcane: Silences targets for 4 seconds (prevents abilities)

• Cold: Freezes targets for 2 seconds (Duration can be affected by talents, etc.)

• Fire: Sets them on fire, fire DoT (tick rate scales off weapon speed)

• Lightning: Stuns targets for 2 seconds (Duration can be affected by talents, etc.)

Poison and Holy presumably have effects on a critical hit also, but I haven't been able to find info on them.

For the Critical Mass passive, what is meant by the "chance" is that it is determined by the proc coefficient of the spell you cast. Single target spells have 100% "chance" to reduce the cooldown by 1 second while AOE spells have differing sets of proc coefficents by spell AND rune. There's a few sites that break down proc coefficents of various spells which applies to crit chance as well as return on LOH. Here, and here. Luckily people with more patience than me seem to have most spells crit proc chance figured out.

Some useful proc chances for popular wizard spells:

Hydra: 0%, Hydras never proc
Magic Missile / Seeker: 100%
Shock Pulse / Piercing Orb: 25% per target hit
Blizzard / Snowbound: 2% per tick per target hit
Energy Twister / Wicked Wind: 10% per tick per target 
Explosive Blast / Chain Reaction: 11% per target hit per explosive (of 3)

I've recently been trying the Windup Wizard/CM build which still seems pretty effective, and a bit silly (in fact it was the easiest way for me to beat inferno Ghom). From personal experience I've found that on my wizard, when I run over 40% crit chance while using a build like windup wizard, everything is off cooldown pretty much all the time.