I have a well-established gadget fetish, so I don't think I'm likely to want to go without a computer any time soon...
But I'm not really in it for the stats. I occasionally check my average speed at the end of a particularly unusual ride to see if it was as fast/slow as it felt, but I certainly don't keep a record. (Though I have been paying more attention to this recently, to compare my darkside vs upright performance. At some point that'll even out and I'll lose interest again.)
What I actually find I use it for most is the instantaneous cadence and temperature displays while I'm riding, as these are useful indicators of the level of stress on my Stupid Knee and Stupid Lungs respectively. And the clock, when I've got a train or similar to worry about.
The overall odometer is handy for keeping track of component wear, and to see how much riding I've been doing generally (if only because people keep asking).
But what I really like are GPS tracks, for that peering-over-a-map-to-see-where-I've-been factor when I go somewhere new. I *really* like peering at maps.