My initial motivation (which remained my motivation for a long time) when I was 12 was a combination of factors. Firstly, looking up to strong heroes like Superman, as well as my father, who has what I can only describe as "dad strength." According to Dan John, you too can get dad strength from practicing the olympic lifts...I think Dan John forgot to mention the caveat that you need to practice said lifts with boulders, or at least with unevenly loaded, stiff, crooked, rusty bars that haven't been safe to use for 80 years, so I'm still lacking in any dad strength of my own.
At the same time as looking up to men (real or fictional) with what I considered to be great strength, I was a seriously underweight child (I weighed 25kg when I decided to do something about it, and I distinctly recall 3lb dumbbells being hard to lift overhead) and was the most readily bullied person I've met as of yet (not strictly related, but not mutually exclusive issues, either).
So, starting out, and up until I was at least 18, my main motivations were to become the ideal of manhood that I'd grown up with (which invariably looked strong, and in practice was much stronger than looks would suggest) and to escape from perceived weakness. I had issues with both physical and mental weakness (the latter was a much bigger player in the bullying I endured as a child), and both the physical and mental aspects have been areas where I've dedicated a lot of time to development.
When I was 18, for about 6 months I was too penniless to have a gym membership, and in hindsight I'm glad that that was the case. From the age of 16-18, the further I progressed, the further I exhibited signs and symptoms of body dysmorphia -- the more muscle I had, the more ripped I became, the stronger I got, the more I obsessed over how muscular and strong I wasn't. This is something I look out for a lot in other young trainees, because I know that most people who haven't grown up with an athletic background get into fitness to fix something, and if you're looking in the mirror for something to fix, you will find it.
My time off was enough to break the habit -- I had been used to leg pressing over 200kg, so I knew that doing some body weight squats wasn't going to build or even maintain the muscle and strength that I had; I'd previously worked up to doing 150+ push ups, and knew that I was beyond the point of getting stronger from them, too; so I basically just had to accept my losses and focus on other stuff. When I returned to the gym in the second half of 2007, I did something that no 18-year-old has ever done before: I exercised with a focus on being healthy.
From late 2007 to early 2010, just being healthy was my main focus. Since then, not getting osteoporosis has been a permanent motivator for me. I thoroughly enjoyed training (although, even before that when I was bat**** insane over it, I still loved it). In 2008-2009, I was doing my Diploma of Fitness. First semester I bulked up by about 7kg without even meaning to, and that was a happy accident. Second semester I started bulking intentionally, and within a couple weeks I could tell that I was lapsing back towards unhealthy thinking patterns, so I stopped, and just worked with the weight I had. This occurred a couple more times, and then I spent pretty much all of 2009 letting my weight sit at about 62kg.
In early 2010, I got reinvigorated about getting as strong as I possibly could, and accepted that in order to be as strong as I possibly can be, I'll need to be heavier. I started bulking again, and for the first time (other than my accidental bulk 2 years earlier) I didn't freak out about it, I guess because I wasn't doing it to look a certain way, but just to be able to move more weight. Since then, I've been able to gain or lose weight quite deliberately without losing my head over it.
I'm much more confident now. My inner strength and outer strength have both come a long way. I'd still like to be stronger (in both respects), and have some specific goals for my physical strength, but being a jillion times stronger is no longer something I feel the need to achieve. I still love training, very much. I'd hate to not be able to train. Getting to the gym and lifting is an end unto itself, although I certainly like what it does to my looks and performance (except for when it hurts me, but I forgive it). Around the interwebz, there's some arbitrary strength standard, that you need to press 60kg, bench press 100kg, squat 140kg and deadlift 180kg. For a long while I chased after those goals, so that I could be "good enough." As I've approached those numbers and discovered that most people in real life are horrified by the thought of ever lifting that much, I've realised how much numbers don't matter. To the general populations I'm Hercules (which I've become especially aware of this year as I've started competing in powerlifting), to the people who think that those numbers matter, coming close to them or having achieved them still doesn't validate your existence, and even if that weren't the case, chasing goals just to look good to strangers on the net is one of the sillier things I've ever done.
I think that all roughly amounts to: I started doing this because I felt I wasn't good enough, now I do it not to be "good enough" for anyone, but because I love training and I love myself. In saying that, if I was in a relationship, she would be an important factor to consider in how I direct my training -- I may not do this to gain people's approval anymore, but if there were someone special in my life I'd certainly want to use my time and effort in a way that's pleasing to her, rather than in spite of her.