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.
Okay, back to vultures. So they're carrion eaters, and I know, that's gross, but they're providing a valuable service. Have you ever seen a vulture's feet? They're completely featherless, all the way up. In fact, they also defecate directly on their feet. Yes, yes, I know, gross. But actually, their stool is incredibly acidic, to the point where it will kill literally anything they may have stepped in while wading through rotting meat. In fact, vultures will typically stay near their meal after gorging themselves, which guarantees that they will be sterilizing their feet after every meal. They act as nature's containment and disposal unit for any diseases the dead animal may have been carrying or anything that might have taken root after it died.
Also, their heads are kinda rubbery. I know, the turkey vulture at the zoo (Toulouse) liked me and would rub his head against my free hand during feedings. We actually experimented with the whole sense of smell thing by having one of the other interns, who Toulouse hated, put on my jacket while handling him. He didn't go for her eyes, or even bate, which was a noticeable improvement over his normal temperament. And trust me, when a big, fully flighted bird bates, it sucks... I had a golden eagle spook on me after clipping and coping, I thought she was going to take my arm off... (all of the birds at the zoo are rescues, and only a small number of them are physically capable of flight, usually due to a bad run in with a car or a hunter)
Oh, and if you're in North America and ever see a bird circling overhead, take a look at the shape of their wings and impress your friends with the following observation: a vulture's wings are long and straight, with tapered tips, they soar and wait.