I do competitive trail, which is different, but I am hoping to do some limited distance (25 mile) rides next year - the thing I like about both sports is that it can be whatever you want it to be. It can be racing to be in the top 10, it can be working to do better than you did last time. It can just be about spending time with your horse testing your mettle. For me finishing well means coming in under the allowed time, with a horse that is happy about being there, sound, and ready to keep going. It means pushing myself to the limits of what I think I am capable of, and it definitely means having a good time with my horse, because it isn't worth it if we aren't having fun. It's also about knowing my horse, knowing how far he can go, how to ride him to his potential, and when it's time to throw in the towel.
I personally try to ride alone on my rides because I think it's important to "ride your own ride" - if you go out with someone else, you often try to match a pace that doesn't work for you and your horse. Some people pace together well, though, and like to ride together, so it's about what works for you.
The multi day rides around here are considered competitive trail rides, which are a bit different rules-wise than endurance - here (VT/NH), endurance rides are done in a day.
Usually people will trailer in the day before and either stable their horse at the facility the ride is out of, or they carry temporary fencing with them to keep their horses in for the night. People will generally camp out with their horses and then vet in the next morning if they haven't done so the night before.
You get stopped along the way to make sure your horse is still doing ok, and pulled if they are not - nobody cares about you though, you could be lame in both legs and on drugs and not get pulled =P
There is also a kind of riding called judged pleasure rides where you do have to do a set distance and a set number of obstacles that you are judged on throughout the ride.