Are lenses on Nikon DSLR cameras interchangeable?

I've been looking at a bunch of different Nikon lenses and am wondering if they are all interchangeable? Amazon has certain lenses suggested for certain cameras, but then with other cameras they aren't suggested. Will this lens:

http://www.amazon.com/...000HJPK2C/

which is suggested for the D90, work on my D3000? All the lenses I'm looking at are new on Amazon, so I'm talking new lens to new lens comparison…

Yes it will work on D3000.It's a AF-S so it will auto focus on the D3000.

As long as it's a Nikon lens, it will work on a Nikon SLR camera.

They should all be

Yes, they are interchangeable. Such is the problem with Nikon. They have some cameras that do not autofocus certain lens models. Check out this page for reference.

http://www.kenrockwell.com/...y-lens.htm

I would consider Sigma 70-300mm f/4-5.6 DG APO Macro Motorized Telephoto Zoom Lens for Nikon SLR Cameras

Lens Construction 14 Elements in 10 Groups Angle of View 34.3 - 8.2 degrees Number of Diaphragm Blad