In the world of gaming, a single die isn't going to do you much good -- you need dice sets -- preferably lots of them! Different RPGs will require a different dice set, and while none of the standard sets ever get you all of the dice you really want (and really, is there such a thing as enough dice?) each of the different dice set types out there give you all the basics that you really need to to game.
Here's a list of the different standard types of dice sets, all of which we carry at Awesome Dice. After the dice set, we'll list some of the common RPG games that use that dice set. Of course there are hundreds of RPGs out there, but we'll try to list some of the more popular games.
It's worth noting that there are some games out there that use very minimal numbers of dice and don't really need entire sets. Additionally there are some games that use only one or two dice for most things, but in some situations use more, at which point you really want a set. Eclipse Phase mostly just uses percentile dice (or a d100), but when rolling damage you could certainly make use of a handful of d10s. Call of Cthulhu also uses percentiles for most rolls, but various damage and sanity rolls make use of the full range of gaming dice found in the 7-dice set.