People still play Warcraft III. In fact, heaps of people play it. If it's not your run-of-the-mill tournament play, then it's DoTA, or tower defense, or some other popular custom map.
Blizzard has seen fit to reward their loyalty by removing the initial CD check from the game's start-up. That... and the company realised the game has been out so long, that those who wanted to pirate it did so a long time ago.
You may remember Blizzard removed the CD check from its RTS Starcraft late last year. Seeing as players of both games spend most of their time on Battle.net, which requires a legitimate CD key to use, the check has simply become an annoyance for paying customers.
Warcraft III Patch Announcements/Updates [Warcraft III forums]