In reply to Alyson:
If indoor climbing is counted as training, and I think done the right way it can be, then I'm primarily motivated purely by the fact I love climbing. I wish I had more time to go and that rest days weren't necessary so I could do even more.
I'm motivated in part because climbing harder means there are more routes, and better routes available at higher grades. I don't have a lot of easy (for me) stuff to do in this country and its hard for me to climb abroad most of the time. But regardless of that pushing oneself to one's limits is what makes climbing interesting so I'm always motivated to try hard and push myself purely because that is more interesting.
The interesting thing about climbing (as opposed to running etc.) is that the competition is with the rock rather than directly with another person. So I think its appealing to people who are not that competitive or like to shy away from direct competition.
In terms of other training currently I'm not doing enough. But one motivation is avoid injuries. Another is related to accelerate general improvement. Just climbing it is easy to plateau and improving some strengths like core and antagonists is hard to do by climbing alone.
I think for that kind of training a diary is a key motivational tool. It motivates to go beyond what you did the past workout. And longer term its motivating to see how much stronger/fitter you are now than in the past, whether that was one month ago, one year ago or when you started.
But overall I'm completely motivated by the passion for climbing and if I was just doing it for some hazy reason like feeling fit and strong I'm not sure I would be motivated at all. Climbing is a good way to express and feel those gains in strength and fitness. When you can do things you couldn't do before that feeling of accomplishment drives you to continue the hard work.