I think the definition of normal has already been flogged to death in this thread, so I won't go there again.

However, should someone try to be normal? That's more interesting.
While in principle I agree with Dervish and Protagonist, I find that principles and reality don't always match up. Yes, we should all simply be individuals, acting neither for or against society simply for the sake of it - as long as our individual desires do not fall too far outside of society's "norm". What happens, however, when your beliefs and desires [i]are[/i] extreme in some way?
It may well be better for the lonely goth kid to put away the makeup and trenchcoat, go out there and make some friends without being ridiculed or feared for his appearance and interests, even if that's not being "true to himself". He's potentially more likely to be productive to society, beneficial for his community, and happy in himself if he does that, rather than being isolated or ostracised.
I'm always very much torn on this issue. I'm fairly fiercely non-conformist (not anti-, [i]non-[/i], i.e. what Dervish was saying about neither conforming nor not conforming for the sake of it), and have received my fair share of shit from people for being different from many of my peers, but sometimes I think being "true to yourself" can actually just make you less happy. I know that if I relinquished my principle of non-conformity a little bit, I'd probably have gotten in less trouble at school and would have avoided a lot of unpleasant things. Sometimes, despite the principle, conformity just for the sake of conformity/fitting in is a good thing, and can be positive.

tl;dr: In principle, yes, be a non-conformist, as Derv and Protagonist outlined. However, in reality, sometimes principles have to be loosened to actually get the best and happiest outcome, because principles are black-and-white and reality is not.