This list is not exhaustive; any idea that is interesting and non-trivial is potentially possible. Use your imagination. I'm happy to discuss possible ideas with you.
Implement one or more non-trivial algorithms, e.g. from the Algorithms and Data Structures class or the Introduction to Algorithms book. You should deliver these as a set of classes with public methods that provide a convenient interface for callers, along with basic documentation and some tests that demonstrate that your classes work correctly. Some possibilities:
balanced binary trees (using AVL or red-black balancing)
linear algebra: solving linear systems, inverting matrices, LU decomposition, least squares approximation
number theory (primality testing, integer factorization)
computational geometry algorithms (finding intersections among a set of line segments, convex hull, closest set of points)
Create a simple utility application for editing or managing some sort of data, perhaps with a graphical interface. Examples:
calendar
address book
personal finance
text editor
Write a drawing/painting program that lets the user draw lines, circles and other shapes in various colors, fill in empty spaces with a certain color, and perhaps perform other graphical operations as well (e.g. adding images).
Implement a strategic board game that lets two players play against each other, or one player against a computer AI, with a graphical interface written using Windows Forms or GTK. Some possibilities: chess, checkers, 3D tic tac toe, Pente, Quoridor, Gobblet. Here is a list of many more.
Implement a simple video game using Windows Forms or GTK. You could attempt to recreate a classic game such as Tetris, Space Invaders, Missile Command or Pac-Man, or you could invent your own.
Implement a one-player puzzle solving game with a graphical interface. Examples: Sudoku, solitaire, Minesweeper, 2048.
Write an interpreter for a tiny programming language, e.g. one with only variables, if statements, and while loops.