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The objective in normal sudoku is to fill each row, column, and contiguous square regions with a certain series of numbers. Ksudoku also has a variant where the regions are not squares, but they are still contiguous. When I say contiguous, I mean each square in the region touches, directly or indirectly, every other square. So the two variants are like such (with each number marking the appropriate region):

However, there are other sudoku variants where the squares are not contiguous that look like fun to me. They wrap around the edge of the grid, so part of the region is on one side of the grid and part is on another. Here are some examples: