It really varies by property, what they're used to doing, and how busy they are.
Typically they block rooms a few days ahead. If they are going to be busy, they know if someone else will be in your room or not. If not, getting a late check out is easy. If that other person has already checked in and the "room was not ready" - well they are going to want you out ASAP.
Usually most hotels will not discuss late check out until the last day. An hour is always granted. (MVCI's are the exception here). I've had as late as 9PM. Most want to charge you beyond 6PM, although the number of times I'ved needed that is very small.
Last trip we requested late check out for one of our rooms and got it extended from noon to 1:30PM, which is all we needed.
Early check-in is almost always 100% successuful - even at 8AM.
Billy
PS - another trick I've used in the past is checking out - then doing something like skiing all day - then back to the hotel to use the showers in the pool area. Done this many times in SLC, and they don't mind letting you have access. So if all I need is a shower later in the day, I will check out, then come back later in the day...