Other than a nice broke horse, I think the most important thing you can have on a ride is a rope. Of course this is mainly for western riders that have a saddle they can do at least a little pulling with. I always carry a rope, even if I don't need to rope a cow.
Here's some things I've used a rope for on a trail ride:
-Pull fallen trees off the trail
-Extract stuck horses out of the mud, sandy creek, etc.
-Spank a dog that wants to chase horses. (or rope the dog and give it a good lesson)
-Use your rope to pull or help encourage a reluctant horse across a ditch or other obstacle.
- Sometimes we take turns following each other and roping horse's hind feet. That way, if that horse ever gets a leg hung in a fence, he won't panick and shred his legs
So what's your favorite thing to have on a ride?