Carnegie Mellon and Penn State support several related projects. Some names associated with this topic are Kurland, Trigg, Davida Charney and Chris Neuwirth.

Basically, as you might suspect, there seem to be good and bad effects associated with using computers. One point is that the specific writing tools being used have a huge effect on the outcome, so it is hard to talk about computers "in general". However, some fairly general findings are: 

People using computers to write tend to revise more, but the quality of the final product does not change significantly. However, if you just want to get people to practice writing, they do tend to write more. The down side is that people get caught up in activities like formatting and font styles which are peripheral to the goal of writing better.

Some systems designed to support particular tasks can be quite useful. For instance, there are some hypertext tools which guide novice writers through heuristic activities supporting critical thinking and analysis which seem to be effective sometimes. Practice is a very significant factor. 

Cochran-Smith, M. (1991). Word processing and writing in elementary classrooms: A critical review of related research. 'Review of Education Research', 61 (1) 107-155.

Bangert-Drowns, R. (1993). The word processor as an instructional tool: A meta-analysis of word processing in writing instruction. 'Review of Educational Research', 63 (1), 69-93.

Kozma, R.B. (1991). The impact of computer-based tools and embedded prompts on writing processes and products of novice and advanced college writers. Cognition and Instruction, 8, 1, 1-27.

Lohr, Linda; Morrison, Gary R.; Ross, Steven M. (1995). Using a Hypertext Environment for Teaching Process Writing: An Evaluation Study of Three Student Groups. Educational technology, research and development. v 43 n 2.

Snyder, I. (1993). Writing with word processors: a research overview. 'Educational Research', 35 (1), 49-68.

revised 5/22/98