As someone who plays a few instruments, playing to a click is helpful. But the sound of a click drives me batty, so I usually start with a nice electronic drum sound from a synth/beat machine. After laying down bass, guitar, etc., I'll then go back and bring down the sound of the synth beat and play to the tune with real drums. This lets me respond to the music in a .... well, a musical way. I can spot music where the drums where tracked first (to a click) and then the band plays over it a mile away, it sounds sorta fake. Pop music I speak of, sounds fine for electronic material.
However, some of the most interesting grooves/feels I've managed to record have been me playing drums without a click, and then trying to swing with it on the other instruments multi tracking. I love the results, but if you put a click to it.... would be humorous at best.
But you never notice that anything is out of place, everything seems to flow together.