Games seem to break down on this line fairly often.
On the one hand you have the D&D and D20 games and their various offspring that put a pool of different types of dice in your hands and let you roll D6s here, D12s there, and D20s all the time for everything. It's good fun, and lets you really get your geek on with a wide variety of polyhedral shapes at your finger tips ready for rolling.
On the other, you have games like World of Darkness, Legend of the Five Rings, FATE, Shadowrun, and other assorted games that make pools of a single die type (usually D6s or D10s in my experience) and those are the dice that you roll to determine what you get.
On the mystical third hand you also have single die systems. Games like the Warhammer 40k line from Fantasy Flight Games where you primarily roll a percentile dice, or like Mutants and Masterminds and True 20 where everything is done with a single D20.
Do you have a preference between the three? If so, which one and why?
Personally, I don't.
When it comes to fun, I find rolling pools of dice is a lot of fun. There is joy in the physical act of it, and I find this most clearly when playing the FFG Star Wars game. It is almost child-like the joy I can get from grabbing a handful of dice - D12s, D8s, and D6s - then scattering them on the table before matching and eliminating symbols to find out what I got.
When it comes to practicality though, I like the simplicity a single die can bring. We roll one dice, read the result, compare that to whatever we need to compare it to, and boom we're done. Maybe it isn't as fun rolling a single die, but it can be a lot faster and clearer to understand than the alternative.
Beyond that aspect of number though, I don't much care what type of die is in my hand. I care about what it means for the system (variance vs. PC skill and all that) but in the game itself? Not really.
How about you?