I always check in at T-24 to the extent it's practical- if the flight leaves at 6 AM I may wait till 7 AM the previous day. As others have said, it's one more thing off the list, you're less likely to be bumped, and it may get you into an earlier boarding group even if you have no status with the airline.

I once flew out of HPN (Westchester) on a day when their check-in computers were down. HPN is really too small anyway for the number of people who use it, and that day it was an absolute madhouse. I was never so happy to be able to bypass the check-in chaos (also had a bag small enough to be gate-checked). It was enough to motivate me to make sure that I was always checked in with a BP before getting to the airport. Even if I can't print the BP or use one sent to my iPod Touch, I'll check in anyway and print the BP from the kiosk when I get there.