I thought it best to have a collection of effects animation and techniques done in brickfilms, both stop-motion and CGI.  This can include Minecraft-style effects, since both are blocky, but it's more than just putting blocks together into shapes of the effects you're making.  It's also using the pieces available to create such effects like muzzle flashes and ripples in water and swapping techniques for digging a hole.  MindGame's film directory is an example of creative approaches in animating these effects.

So share what you've done, what you know, and what you've seen in brick-based effects.  Or if you have a request on how to animate an effect in LEGO/plastic construction toy pieces, ask it here and hopefully someone can share their knowledge on it.

For posterity, I'll update this post occasionally with a list of links to said examples and techniques.  Organization and formatting shall come about in the future but to start things off, these are what I managed to find so far.

CGI Exploding Plum of smoke

The LEGO Movie effects
Brick Explosion

Plant, round plates and ice creams for Shower and soap bubbles

Ice cream scoops as smoke

Brickified Water animation

Rotating flame piece for fire and tile animation for water ripples in Bound

TBD

• Explosion

• Fire Smoke

• Dust

• Water

• Ballistics