English Exercises was developed by an EFL teacher in France, and has a long list of…… exercises.  I particularly like the “Story Building” ones near the bottom of his site, where students have to “build” a story by choosing from a variety of sentences.

I’ve placed it on the English For Intermediate and Advanced page at the bottom of the Other category (there are such a variety of activities I couldn’t think of a better place to put it).  However, many of the exercises would also be accessible to High Beginners.