All games on the site generally fill on a first-come first-served basis. There are some exceptions to this. Invitationals would obviously be one. The Newbie games have a restriction on the number of newbies/ICs. The VM2 application process could have been another, though it ended up acting more as a way to ensure everyone understood what was expected of them before they signed up.
Some mods do occasionally have requirements for signing up. The most common is an experience threshold - more experienced players are given preference, or new players are excluded entirely. As far as I know, this only happens in Large games, as other types of games have signups handled by the List Mod rather than individual game mods.
On the other end of the spectrum from invitationals is banning specific players. This is fairly rare as far as I know, but does happen occasionally.
I'll leave it at that for now. Please refrain from mentioning specific examples/players if possible.