DotA (Warcraft 3 mod) is an RTS/RPG hybrid primarily focused on team vs team based combat. While it has a bit of learning curve, the game has enormous depth. It is enjoyed by players both at a casual level and at a highly competitive level. The game design focuses on providing players with a game they can play for years and still feel they have room to improve, and to do it in such a way that doesn't compromise the overall enjoyability and playability of the game in the process.
If you are new to the game, it's recommended to play against computer bots with the AI Maps for the first few times. However, the real fun starts when you play against other real players.