The majority of portraits are done with a telephoto lens, the exception of course being environmental portraits where the subject is a person in the context of their surroundings.
Telephoto lenses pretty much get rid of the surroundings and they do this in a couple of ways. The first is that telephoto lenses have a very narrow point of view so you're pretty much focussed in on your subject and any distracting elements on either side of them are cut out of the picture.
Here the young mother and her son were actually surrounded on both sides by other people feeding the pigeons but by going to the 70-200mm zoom I managed to cut the other people out of the picture and produce an intimate portrait of just a mother and son.
The other thing that telephotos do is give you a small depth-of-field so that what you focus on is sharp but everything in the background and foreground goes very blurry very quickly. This also helps get rid of distracting elements in the background. In this particular case there was a big pile of junk (I can't remember what exactly it was now) behind them and you can see it in the top left hand corner but because it's so blurry it doesn't get in the way of the portrait.
And don't forget that with the compression perspective that telephotos give you the pictures are very flattering. Who wants their nose to stick out any more than it has to? Use a long lens and it will be flattened (as long as they're not side on that is!).
The other way a telephoto lens can help portraits is by giving you a little bit of distance if people are uncomfortable being photographed. When you've built up a rapport with someone you can often get up close to do some nice wide-angle, environmental portraits but before you get to that point you might find it easier for both yourself and the subject if you can stand back a bit and be as unobtrusive as possible as they get used to you photographing them.
So if you're taking portraits of people start off with a telephoto. Somewhere in the range of 105mm is a great focal length for really flattering portraits. I've heard a rumour that the Playboy photographers shoot their stuff with a 600mm but I'm guessing that has more to do with preventing accidental touching than it does a desire to flatten anything. :)