That depends. If you are referring to recently released mainstream games the
answer is almost certainly no. If you are referring to 1990s mainstream games
like Doom, Wolfenstein, Quake, and others most of these games have been
free'd and will work with free drivers or do not require 3D acceleration.
There are also quite a few free software games out that aren't that terribly
old. Some of them are so new that the free drivers aren't capable of handling
them yet.
If it were easy everybody would switch to free software. It's not easy. It's
a slow process for most. There are lots of entertainment options though from
movies and music to games. Instead of following try leading for once. Try
making some new friends. This is of course harder to do than simply following
the pack.