What about making a noughts & crosses/tic tac toe game? There is no requirement for proper graphics, just nine buttons on WinForms.
You can have multiplayer modes, including victory detection, and a single player mode with AI. If you wanted to learn about networking, add in a multiplayer mode over the internet, with highscore lists too perhaps (quite what counts as a high score, I don't know: number of games won, or something? It doesn't have to be meaningful to teach you valuable lessons though....)
Alternatively, look here: Martyr2's Mega Project Ideas List! - Share Your Project | Dream.In.Code
