You could do matrix-based combat... Which is generally described as Rock, Paper, Scissors on steroids.
So you come up with a list of 'moves' that each player can do. You can have them sent to a third party, or you could try to have a program that accepts input from each player secretly, and when it has both moves, reveals them both to the players.
Here's an example I've seen done in chatrooms before:
http://www.duelingzone.com/dz/tools/dommatrix.pdfBasically, a hit is 1 point, and an advantage is 1/2 a point. Players play until someone is at 5 or greater AND ahead by a full point, OR until 15 rounds are up, in which case, it's a draw.
The interesting thing about these sorts of games is that they are more interesting the less uniform they are. RPS is 100% uniform, so there's really nothing to think about with it. But in an unbalanced version of the game, certain moves become popular because they have high success rates. Then, with time, people start using moves that are weaker themselves, but strong against the popular moves. Strategies can develop, and the whole thing gets fun and exciting!
...Atleast it does to me <.<
EDIT: I forgot to mention the best part, which is that the moves themselves can be very generic. In that way, descriptions of the action can be 100% written by the characters. So a mental blast could have no visual component if a player wanted... or it could be a purple beam, or a green-lantern style glowing boxing glove that punches something. The possibilities are endless!