I go with the "depends on the situation" school but its been a few years since I used a double handed rod in fresh water.
I would probably go with a double hander purely for the fun of it unless the size of the stream forced me to go with a single or accuracy is at a premium as Topher points out.
A lot gets written about the prodigious distances which are possible with a double handed rod but that's only part of the equation. Being able to present a fly, under control, at distance, and effectively cover a greater area of water (and fish) is where the advantage really lies (IMHO).
When sight fishing, look over your shoulder from time to time, you never know who's behind you