There are several things I like:

• Combining tools. That can be the combination of a few shell command, or it can be the integration of a blog system into my offline CMS.
• Logical puzzles and riddles like Sudoku or Nonogram both manually and by program
• Quickly coming up with solutions to data munging problems that make all non-perl-programmers gasp
• Solving tricky logic problems with programs
• Making seemingly simple things really useful. For example I maintain (and mostly wrote) the IRC logs for #perl6 and #parrot, and it features far more details than you might see at first, each of which added after a feature request. Not only URLs are turned into links, but also stuff like S03 into S03, revision numbers into links to the appropriate changesets etc. This is mostly not challenging from the programming point of view, the real challenge is to identify what's useful

I'm sure that there are many more that just don't cross my mind right now. Basically everything that makes me think, and that has visible results.