Specializing?

I am just wondering if it is true that it is those who specialize that will come out ahead career-wise. I have never been the type of person who specialized in anything, I like doing a little of everything, which is why I do technical support. I’mfeeling rather burned out at this point in my life, having done this for about 8 years. I’m not sure in which direction I could go, considering I haven’t a degree, nor do I have any certifications. My ability to be self-motivated and a quick learner, along with my incredible patience and common sense skills have kept me employed even in this economy of downsizing. I would like to hear where some people who started out in technical support ended up, and how they got there. Thanks.