For our upcoming game The Meddlers, we opted for d4 dice pools as the core mechanic. Here is the basic rule:
The core mechanic
The core mechanic of The Meddlers is quite simple, you roll a pool of four sided dice* against an opposing pool of four sided dice. Both sides take the single highest result and compare them. If the aggressor meets or exceeds the result of the opposing pool she succeeds. Sometimes this will be rolled against another character’s pool, sometimes the GM will roll a pool to reflect the difficulty of a task when it isn’t against a foe. The Aggressor is always the person taking action, attacking, etc.
The main reason we picked D4s was aesthetic. Four-sided dice feel diminutive seem appropriate to a game about Brownies. The other reason is I've long wanted to use d4 as the basis for a game because of the tighter range. Because the game favors the aggressor, the system leans toward success, which makes for fast play.
Here is an example from a playtest I was running. This is from a combat between a Brownie Thick-Hide and a Red Cap. The Brownie is attacking this round. Because the Brownie has a Brawn of 1 and a Melee Skill of 2 he rolls 3d4. The Red Cap has a Parry of 1 and Brawn of 1, giving her a Defense of 2d4. Both roll and take their single highest result. The Brownie's highest result is 3, while the Red Cap's highest result is 1, meaning the Brownie succeeded and now gets to roll damage.