How often they get stuck varies from character to character.
I'm leveling a shadow priest right now and he's flying through the quests and only gets stuck in Orgrimmar. For some reason, every character of mine that uses Kick's profiles gets stuck at the elevator forever unless I manually put him on the elevator. Once he gets to the top, it's fine as he can make it down the elevator by himself. He'll also get stuck in Ashenvale sometimes because he gets too close to an Alliance Night Elf camp that has high level guards around it.
You aren't going to have an afk 1-90 solution unless you use something like Pangea's grinding profiles, but those get stuck sometimes too.
If you're leveling a character that can heal, just go healing spec and do dungeons from 10-90. Your queues will pretty much always be quick and you'll stay geared if you don't have heirloom gear.