There are many different thoughts on this question. The last two issues on Flyfishing and Tying Journal (an FAOL Sponsor) both had issues on fishing downstream. The Spring 07 issue had an article on general downstream presentations by Dave Whitlock. Basically (very basically), yo can approach it in four steps:

Approach
Presentation Prep
Downstream Presentation
Striking with the Downstream Presentation

The Summer 07 article dealt with nymphing downstream rather than upstream written by Rich Osthoff. It covered the advantages you gain by using a downstream presentation. Some of those listed are:

Faster prospecting when trout are feeding opportunistically
It puts the nymph in the point position
You can swim the nymph across the current on a tight line
You can slow it down to give trout in fast water a longer view
You can control the attitude of the nymph
etc

They make a lot of sense to me. Of course, we all know that trout love to make liars out of our mentors. If you're hitting trout water and the opportunity presents itself, try both ways. Let us know which worked better for you....and where