Passing on some stuff I've heard from a self-defense instructor:
Don't be afraid to be loud and make a scene if a guy is bugging you. Usually that will deter him. Don't just say "Leave me alone!", also say "I don't know you!". People in a crowd will often assume a man and woman yelling at one another are a couple and not want to get involved, but are more likely to interfere if they realize he is a stranger to you.
Also have your cell phone handy and don't hesitate to call the police if he won't quit. The simple act of calling them will often send a creep running.
Violence should be a last resort, but if he just won't leave you alone, use it. Don't try to fight him, try to hurt him and then run away. Aim for sensitive areas- instep, groin, eyes, nose. You don't need to buy a knife or gun; if you're not comfortable using whatever weapon you buy it's more likely to be a liability than an asset. Do use the "weapons" you have on you- fingernails, keys, teeth if necessary.
I hope that helps! I'm a guy, and average-looking, but even I get pursued by persistent guys now and again. Some of them are harmless and just don't know when to quit, but others are real creeps. One thing I've found is good for turning away the first is to not be quiet or smile when saying "No", they may take it as coyness. There's no need to be rude when someone's just asking, but do be firm and serious.