I've just been thinking about this for a while. Every single person I've spoken with would go traveling with the Doctor as his companion if given the chance. I always end up asking them if they have or have not considered the danger that is constantly involved. They would still go. That's something the Doctor actually asks his companions too--about the danger and they answer in the same way. I have three reasons that range from the petty, the practical and the profound.
The Petty: I can't drop everything and go. That's been my issue for a lot of events forever, but I can't drop it and go. I can't come back and adjust. I'm not good with change... and what is travelling in the TARDIS but constant change?
The Practical: I wouldn't last. How many times has the Doctor said "RUN?!?" to his companion? At the state my cardio is at, I wouldn't last a day in a zombie infestation, not to mention outrun aliens with the Doctor. I've also seem Martha run in heels. ...Martha. How.
The Profound: I don't know if I can handle it. I know I can't handle the physical... but knowing about the worlds out there? I don't know if I can handle that. In each episode, the Doctor and his companion goes on a dangerous journey and I think I'd become so exhausted. I'm not one who runs towards danger. I walk away and I would only look back from behind a very safe wall.