Can a Nikon d3100 and a Nikon d60 share lenses?

I'm looking to buy my first dslr (Nikon d3100) and I wanted to know if I could use the lenses my sister already bought for her Nikon d60.

Yes.

Only with her permission.

Yes indeed. Since neither have built-in focus motors, it is likely your sister only has AF-S lenses, which are required to autofocus with either camera.

Yep, but only motorized lenses work on the d60 and the D3100. Both have no screw drive motor for simple lenses. So if your sister has 3100 functional lenses they work on the D60 as well. It is the same camera with 10 mpix instead of 14 mpix the 3100 has. Body is identical.