Rummy is fun!,
There are many different versions of Rummy. They all consist of building melds, which are runs (straights) or sets (three... or four of a kind). My personal favorite version of Rummy is Ruckus, which is dealt with seven cards, rather than ten. Your opponent has an opportunity to build off the runs and sets you lie down, since you discard them during the course of the game, rather than at the end when someone knocks.