In the classic series, dozens of rooms were seen and discussed and in some cases jettisoned. Each companion (after the first few) usually had their own brand-new room, although sometimes an old one would be reused. We were also told that the TARDIS can reconfigure its interior on the fly. We even saw the Doctor get lost in his own TARDIS.
In the revived series, we've so far seen two console rooms and the wardrobe, as well as a long series of corridors, plus a few more rooms in the Adventure Games, and we've been told about many more, including the swimming pool, the library, at least 7 squash courts, etc. And there's no reason to believe that the 11th Doctor's TARDIS is any smaller on the inside than the 5th's. We've also been told that the TARDIS can restore old rooms from storage, even if they haven't been stored yet.
In the non-TV stories, we've seen a lot more rooms, and even seen the TARDIS turned inside-out to become a city. It's been said to be 'potentially infinite', which might imply that the number of rooms it can have is unlimited, even if the number it has at any given time is finite.
For a (possibly incomplete) list of known rooms, and much more information, see tardis:the Doctor's TARDIS.