Cross processing is developing film in the "wrong" chemistry, for example shooting slide (E6) film and processing it in the chemicals meant for colour negative (C-41) film. This is normally what’s meant when people say cross processing, but it can go in almost any direction. You can also do C-41 film in E6 chemistry, or any film in B&W chemistry. The only thing you can’t do is B&W film in colour chemistry, because the bleach leaves you with a blank roll.
Apparently "film acceleration" is a bit more complicated, and sounds a lot like something called the "Henry Beck process" that the owner of my local lab told me about (and I can find absolutely no information on anywhere). Instead of a simple chem switch, this is: underexpose slide film, pre-soak, soup in B&W developer, wash, fix, wash, bleach, C-41. Yeow! But the results do look unique.
Read the how-to, with sample images, at JPG Magazine.
Flickr member pochedunfou also has a large set of accelerated photos, which serves as an excellent reference of the effect across a number of different emulsions of varying age.
Update: pochedunfou pointed me to the Be Great: Accelerate group for the technique on Flickr. Cool!