The answer here can't be precise. You can play Windows games on Linux using softwares such as Wine (free) and CrossOver Games (paid), that simulate Windows's APIs.
The performance in some games are actualy better than playing it in Windows, like Counter Strike 1.6 for example, but lots of games simple won't play. There is a software database that shows lots of softwares and games that run with Wine, with how tos and stuffs.
But be aware that Wine can be tricky and kinda depends on your hardware. A game may play fine on NVidia graphic cards but not with Intel ones for example, even if it used to play fine on Windows.
On a side note, Warcraft III received a platinum score on Wine App DB, so i would say it play just fine, but never tryed it myself since i prefer to play native Linux games (and trust me, there ARE lots of them).
Wine is on Ubuntu's repositories, so all you have to do is type this on terminal:
sudo apt-get install wine
The Wine App DB can be find here. You could also look at PlayOnLinux, a front end to Wine that implement lots of the how tos and do it themselfs, prety cool. And if nothing of that helps, you might want to try Cross Over Games, a paid software (: