Hmmmm.
I like Palladium's phased combat system. One person attacks, then the other person defends. If that defense takes an action (is a dodge), then they lose their next attack and are forced on the defensive until next round or their can turn the tables on their attacker.
I like the dice trick in Silhouette and ICON, rolling a bunch of dice and taking the highest. Silhouette has a better way of dealing with critical successes (if any other dice other than the highest roll 5s or 6s, they each add one point to the resolution total). But ICON has the dice trick the right way around with Attributes determining number of dice to roll and skills being directly additive.
I used to really like the damage and staging numbers in Shadowrun 1e. Basically, each weapon did a base damage, say Moderate. A single success on the attack roll would indicate this base damage was inflicted. But for every number of successes equal to the staging number of the damage (a number between 1 and 4), the damage category went up. So, if I had a weapon that did Moderate base damage, and had a staging number of 2, then I could do Deadly damage if I rolled 5 successes on the hit roll (1 to hit, 2 to upgrade to Serious, and 2 to upgrade to Deadly). At that time it was really novel to have the attack roll determine the base damage as well.
I tend to like rolling lots of dice. It makes me feel like I'm doing something big when I have a handful of dice to roll for an action. So, I enjoy playing dice pools.
When I design my own games, I usually go with the old tried and true attribute + skill + die roll against a difficulty or opposed roll. For my starship game I use a die pool which functions almost exactly like the old Storyteller system. Although it looks like I copied the mechanic, it was more of a parallel development sort of thing.