ORIGINAL: Blades
I think that for a drummer, playing to a click is unnatural. It's far too rigid and disciplined They like to play slightly ahead or behind a beat, even if it's milliseconds, to give the tune "feel".
If you are a GOOD drummer, the click should not prevent you from exploring the territory just before or after the beat to get that rushed or laid back feel. If anything, it's helpful in making sure that you don't over-do it. Sometimes, when playing behind the beat, there's a tendency to also slow down. The click helps lock that in.
In a studio, especially where overdubbing is used (99% of the time), and double-especially if the whole rhythm section isn't recording together (probably not terribly common, except in things like online collaboration and whatnot, though I have recorded entire drum parts to songs without even a reference instrument, because of studio limitations), the click is absolutely essential. It just turns to a festival of slop if there isn't some reliable time-piece. REALLY experienced bands can get away with this, but odds are pretty good that THAT drummer is capable of playing comfortably to a click as well. 
Agreed. Good post Blades. You bring up an interesting point regarding on-line collaborations. Exploring the territory around the click is absolutely the right thing to do when tracking a rhythm section simultaneously. Because of the push and pull of the other musicians, it acually happens automatically. Everybody plays together and the drummer pays attention to grooving around the click.
However, when replacing MIDI loops and samples with a drummer's performance, the game changes. Many times much of the song is already done to loops or MIDI groove clips that are triggering a drum sampler locked to a click. As a drummer, I've got to nail at least the downbeats and play rhythmic figures pretty accurately. These guys are conditioned to a steady tempo, and wandering too far from the click equals loosing the groove, and they are quick to hear that. There's still plenty of human feel and groove when playing closely to a click. I've only met one or two drummers that manage to play like a robot when playing to a click. Very few can be that accurate. However, I've tracked many drummers that can't play to a click because they've never practiced it, and they don't know their timing is problematic.
In my line of work, the click is necessary and fun. Makes for great recordings.
When I'm tracking a live band all at once and the drummer can't cope, we eventually agree to turn the click off and record a live demo. The band is happy, 'cause that's the way they really sound and they're used to the rushed fills, and wavering time. But to more experienced listeners, it almost always ends up sounding like a demo and not a commercial recording.