I have a full assortment of Nikon lenses that I've acquired over the years. Some of them I use for sports photography. Some of them never see sports duty. And some are versatile enough to be used for both sports and other uses.
My biggest sports lens is the Nikon 300mm f/2.8 AF-S ED-IF. The specific version you see pictured to the right is the ED-IF II version. Nikon has made many renditions of this lens over the years. All have very high quality optical characteristics. There are three versions that are optimal for sports, however. Make sure the version you choose has the "AF-S" designation. AF-S is the advanced autofocus system incorporated into many newer Nikon lenses. As a sports photographer, AF-S is important to you because it provides the autofocus speed that sports photography requires. The current AF-S model Nikon sells today is a vibration reduction (VR) version that's very expensive. You can find a new version of this AF-S VR lens for sale here on Amazon.com. I found my non-VR lens on eBay, and purchased it used for less than half the price of a new VR model. This 300mm lens is always with me at soccer games. It's got the reach I need. Optically, it's second to none. It's fast enough (f/2.8) to work under low light conditions, including high school stadium lights. And I can team it up with my Nikon 1.4x teleconverter or 1.7x teleconverter if I want even longer reach.
My other work horse sports lens is the Nikon 70-200mm f/2.8 AF-S VR lens. This lens is versatile for both sports and other uses. Many experts believe this lens is one of the highest quality telephoto zoom lenses ever produced. If you're taking sports photos of kids playing sports on any field smaller than a football field, this might be the only outdoor sports lens you'll ever need. I emphasize "outdoor" sports because, even as an f/2.8 lens, this lens usually isn't fast enough for sports shots taken in the horrible lighting of school gyms. But if you only wanted to purchase one high quality, versatile, telephoto lens for your Nikon digital slr, this is the lens to get. Find it here at Amazon.
The other sports lens I frequently use for indoor sports is the Nikon 85mm f/1.8 lens. This has become my basketball lens of choice. The aperture of f/1.8 is fast enough to capture the action in poorly lit gyms. Some might find the reach of 85mm a little too long for their needs. But it works for me. You can also find this reasonably priced lens on Amazon as well.
If you find the 300mm 2.8 lens above too rich for your blood, try Nikon's 300mm f/4 AF-S lens. It won't work for you under the stadium lights or very overcast, dark days, but for all other lighting situations it's a great lens.
If you want just one lens to cover all of your outdoor sports at a reasonable price then check out the Nikon 70-300mm f/4.5-5.6 AF-S VR lens. Be forewarned, however. This lens will only work for you during the most optimal lighting conditions. And even then, it won't give you shots where your subject is sharply in focus with the background nicely blurred, which helps to highlight the main subject like the photo below.
I know some of you have Canon camera equipment. If so, Canon has similar lens choices as described above that you can choose for sports photography as well.