My dog comes on trails with me all the time. She lives where my horses are, so it's the only regular excercise she gets. She's a Kelpie, which is an Australian breed bred for working sheep, so she has tons of energy and is very athletic.
She is very well behaved. We bred her, so she was raised around the horses and also learned how to behave and what we wanted off lead very young. By normal standards she is very untrained, can't walk on lead, can only sit and come, but off lead and while on rides she is awesome, will come and sit beside me on my horse, etc. She is really good with other dogs, will sniff for about 2 seconds then leave, or not say hello at all if I call her on.
Problems... Don't really have any. Except if she sees a rabbit :] lol! She is 4 now, and has been coming with me since she was a pup, so she is pretty well adjusted to riding with me. Sometimes I bring her mum and another Kelpie bitch we have with me if I am just staying on the farm... Again, they are sheepdogs, so used to being off lead and have great recall. Flash (the other bitch) sometimes jumps up and tries to bite noses, but a growl quickly stops her.
It's awesome excercise for them, and there is no better feeling than galloping along a paddock and seeing three fit, sleek and healthy dogs revelling in running alongside you.