Like a lot of people here I'm really drawn to a dice pool. They're fun to use, and I want the underlying math of most rolls obscured, while also having some sort of a curve, even if I don't know exactly how the probabilities shake out (Never tell me the odds, etc.).
For those reasons I really hate the flatness of a single d20, as well as a percentile mechanic. Both just seem completely swingy and boring to me.
My current favorite dice pool mechanic is in most Forged in the Dark games, where you're rolling a pool of dice and looking for the highest number. In Scum and Villainy you might roll 2d6 for a given action (based on a rating of 2 in Helm, for example, to fly a ship), then you could add a d6 if you push the roll (taking 2 points of Stress, which act sort of like HP), or a d6 for taking a Devil's Bargain from the GM (get a consequence on the action no matter how you roll, like maybe you'll overload and damage the engines), and so on. If your highest single roll in that pool is 6 you fully succeed, if the highest is 4-5 you succeed with a cost, and with only 1s to 3s you fail and typically take even more/worse consequences. Multiple 6s is a critical success.
That kind of dice pool isn't as empowering as a giant handful of d6s in Shadowrun or Vampire, but it makes for really dramatic moments, with lots of cool ways to increase the tension by adding a die here and there, usually at a cost.
I'm also really into the weirdness of the dice pools in Trophy, which borrow some elements from FitD--including the Devil's Bargain mechanic--but include some unique twists. I won't get into all of the options in the game, but for most actions you roll light and dark d6s at the same time, and the result on the dark dice can mean PCs take Ruin (you usually take five Ruin before you're dead/transformed). Dark dice factor into rolls in different ways, and there's a completely awesome dice pool mechanic where during combat you roll a single pool of dark dice, one for each PC fighting the monster (the game assumes most fights are desperate group efforts against one horrible thing) but each PC also rolls a single light die for themselves. That number is their Weak Point for the fight. If any of the dark dice come up with a PC's Weak Point number, they take a Ruin, or lose a piece of armor (regardless of whether the overall dark dice pool rolled high enough to beat the monster). And if the dark dice roll isn't enough to beat the monster's Endurance, you have to either retreat, find a way to lower its Endurance, or take a gamble, and add an extra dark die to the pool, and rerolling the now-larger pool. And you can keep gambling like that, adding more dice, rerolling the pool, and risk taking more and more Ruin until you beat the thing, die trying, or run away.
It's way too abstract a combat mechanic for a lot of (most?) gamers, but to me it's one of the coolest approaches to making combat scary that I've seen.
