Yes.
I ride mainly on the road, and have been using it as a training aid. The key is not to have one showing you a load of otherwise meaningless data, but to know why you want one.
For me, I have an upper limit based on my threshold (i.e. the point beyond which I go all anaerobic), which is useful. At HTN the other day, it was beeping like hell as I carried up the 45 degree slope after the field.
I have memorized where I need to be in terms of zones for most of my training (esp on the turbo) and otherwise just use it as useful post-ride data. It's quite nice to know that, say 12 months ago, for a given effort my HR was x, but now it's x munis y beats. Shows I'm getting fitter.
I have a Polar CS300 (not sure they make it any more) which is a watch that also works as a bike computer, so I can wear it for general exercise as well as riding.