Just to lay out some basics:
"Cross-processing" is processing a film intended for one process in another one. Common types of cross-processing are E-6 film in C-41, C-41 film in E-6, and any color film (C-41, E-6, or K-14) in B&W chemistry. Some cross-processing, such as B&W or (I believe) Kodachrome in either E-6 or C-41, won't work at all; you'll get back a blank film strip because the bleach will remove the silver and there'll be no dyes left behind.
The result of cross-processing is, to a first approximation, like using a conventional film for the process you used. So if you cross-process Velvia (an E-6 slide film) in C-41 chemistry, you'll get negatives. There are differences, though. The orange mask of C-41 films is a characteristic of the film, not the process, so Velvia processed in C-41 will lack the orange color mask. Likewise if you cross-process a C-41 film in E-6 or B&W chemistry, it will retain its orange color mask. E-6/C-41 cross-processing also results in generally odd colors and contrast. Some people like the effect for certain types of shot, but it's not something you'd ordinarily do if you want "normal" negatives. It's certainly worth experimenting with cross-processing. For more information, try doing a Web search on "cross processing film" or a similar phrase.