On the most simplistic level, I always figured: look, I trained my ear, my sense of pitch is really good...I've payed my dues....NOW LEMME USE A DAMN TUNER!
Actually there are lots of really valid reasons to use (some types of) tuners.
Midchuck's right about guitars never being perfectly in tune. The tuner helps you learn where you have to compensate. If you've got 10 minutes, try this: Tune the guitar open, now try each string on each fret with the tuner. I guarantee you there will be variances.
The autoharp. 'nuff said.
Hammer dulcimer. more than enuff said.
Once again, as 'chuck said, in a jam session it's a great arbiter.
I like the old fashioned dial type as opposed to the LED styles. I like to see that old needle heading to the middle. My favourite for accuracy is the SEIKO. Korg, as well. The really cheap ones that only have "guitar" notes on them aren't that good of a buy, 'cause folks with other types of instruments who are playing with you, can't use 'em. A chromatic seems the way to go.
I'm pretty 'hard ass' about folks being in tune, but I'm told that in Texas they'll string ya up for using a tuner!