Now, I put off writing this until the last possible minute, so it's going to basically just be a regurgitation of facts, some more interesting than others. Here we go...
First off, there are two distinct types of vultures: old world and new world. I'm specifically going to talk about new world vultures (i.e. turkey vultures and condors), mainly because I know more about them off the top of my head. But just as an aside, old world vultures are more closely related to eagles and hawks than their new world cousins, an interesting example of convergent evolution. Both fill the same ecological niche, but while old world vultures rely entirely on their eyes to spot their next meal, new world vultures have an amazingly good sense of smell and can find carcasses entirely by scent when the need arises. Fun fact here: most birds have little to no sense of smell. It's one of the reasons owls can safely prey on skunks. So if you've ever heard someone say that you shouldn't help a baby bird that's fallen out of its nest because the mother will smell you on it and kick it right back out, you can forget about that. Help the bird, or call animal control.