Telephoto lens for NIkon DSLR?

I've just bought a Nikon D3100 14MP DSLR with a 18-55mm lens.
I'm looking for a telephoto lens for shooting wildlife. What lens would you recommend I buy?
Does it have to be made by Nikkor to be compatible with Nikon?
What prices would i be expected to pay?

Added (1). There are so many letters and abbreviations for lenses thats what's really confusing me:-/
All great answers thanks, and keep them coming.

Sigma and Tamron also make lenses for Nikon
For wildlife you will probably want about 300mm or more
Prices can be anything from about 140 GBP to several thousand GBP (with most being about 300-1000 GBP I guess)

Just look around for something 200-300mm at the long end.

You don't have to buy the Nikkor, but you do need to make sure it's in Nikon AF-S mount. Sigma and Tamron will fit if you specify the mount, Canon, Pentax or Sony obviously won't.

The, 'S,' in AF-S is important because it designates a lens with an AF motor - something you need to allow autofocus. Sigma lenses with motor are called, 'HSM.'

AF-S DX NIKKOR 55-300mm f/4.5-5.6G ED VR is a good zoom lens camera. It must be around 400$ or 250 pound.

Although third party manufacture also make lenses for Nikon but i'm not sure about the quality of lens.

I've shot a few seasons with Nikon's 70-300 VR. Fine lens, built extremely well. I've shot in torrential downpours and snowstorms and the lens didn't blink. Looked at the 55-300 when it came out. Nice, compact lens. Optically quite good but not an all weather lens.

Since then I've moved toa Sigma 150-500.It's huge and heavy compared to the 70-300 but the difference between 300 and 500mm is worth it. 300mm is short unless you are dealing with tame wildlife or if you have excellent fieldcraft skills.