These problems might help exercising programming skills in general and could also be used for learning, practising or exploring programming languages. They are similar in spirit to programming katas, but much less thought out. – Just stuff I came across and wrote down. To be honest, I'm mostly publishing them so that I can show off my solutions, which are quite horrible at times. But you should solve them anyway, because then you can show off your solutions without needing to publish exercises first.

• ExTwoRemoves – finding words with interesting properties
• ExUniqueWords – removing repeated words from a text
• ExMaxProbChain – finding the most likely chain of events

The Spare-Time Teaching Challenges are another source of computer science exercises. Probably better and harder ones, though.