I'd want to have speed, odometer(s), cadence for sure.
A heart rate monitor and/or calorie counter would be nice, but I can live without them.
Least important I'd like to track elevation changes and would be nice and I'd like to be able to view the rides on a computer, but that's not terribly important.
GPS doesn't appeal to me at all. I'd like wireless, but I'd be willing to go wired too - depends on cost difference.