Most modern programs won't run under Wine. Many older ones will, though. See winehq.com. Many distros have Wine already installed, but it's a moving target and you'll probably want to install the latest version.
There is a project offshoot of Wine by http://transgaming.com
They've modified Wine to support many games, including Warcraft.
But if you're a serious gamer, you'll need a Windows partition
Personally, I'm so fed up with Windows that I wiped my Windows partition the other week. Sure, I miss gaming, and am often tempted to re-install, but that's how much I hate Windows, that I even hate everything that even RUNS only on Windows, so much so that I'll give up even Windows games.
Of course, with only a 600 Mhz P3, I can't run much that's on the shelves now, but still, I've got about a hundred great games I've bought over the past ten or so years that I'll just have to wait to run.
But I can still play the worlds greatest text adventure game. Linux.