I've had good experiences with United and Delta -- for United, due to a medical emergency, I needed to fly from SFO->JFK as soon as possible -- I called at 5 pm, and was on the redeye that night (no fees). I get the impression that on the day of the flight, if there is unsold inventory, they will release it (even if it wasn't available a few days before).
While Delta does charge a $75 fee, they were able to get me from the Bay area (had to fly out of SJC) to Lima the next day (again, a personal emergency). The weird thing was that my flights were actually overbooked -- they had to kick somebody off both legs of the flight so that I could be on it. (So the $75 didn't even come close to covering their costs...)
[This message has been edited by danM (edited 11-30-2000).]