Many times, I have limited space to pack games, and don't know how many players there are going to be. I frequently end up in a situation in which we have 5 players, but games that only work with 3 or 4 players, or something of the sort. In these situations, games which are flexible in the number of players they support are useful; one or two such games can cover most situations you end up in.
One problem is that while many games nominally work with a given number of players, they are really best played with a narrower range of players. For instance, there are many multi-player games that have a two-player variant, but the two-player variant is quite different than the multi-player game, and couldn't really be called the same game.
So, what games support a wide range of number of players well? Since there are many games which support 2-4 or 3-5 players, let's limit it to games that support at least 4 different player numbers well, such as 2-5 or 3-6 or any odd number from 7 to 15.
edit to add: Let's limit this to non-party games; party games as a genre tend to be fairly flexible in the number of players, so it's not all that interesting to list each one.