These can take many different forms.
Word games - x-words, hidden words or letter, anagrams, etc
Puzzles -
Board games - design one that can be posted online or downloaded and printed out.
Interactive games. These are a bit more technical but can be a lot of fun and a great way to learn.

Have a look at a few games here (PC only). They were written some time ago but still work and are a lot of fun.
The best games start with a simple idea.

What else can you think of here ...?