Will my 35mm SLR lenses work on a new Digital SLR camera?

I have Nikon 35mm SLR camera with a few different lenses, will these lenses work on a Nikon digital SLR?

Yes as long as the lenses are AI or AI-S lenses or later (ie after about 1959) they will mount on a new digital body.

Entry level Nikons - D3000, D3100, D5000 and D5100 do not have a focus motor in the body so you will need to manually focus lenses - some of the older lenses may need manual aperture changing or may not meter correctly.
Mid level Nikon will be able to autofocus any AF lens, but again older lenses may not meter (it depends on lens & camera body).

Along with what deep blue said, here is a complete compatibility chart

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

If they are AF-G lenses or AF-D lenses then you need to think about a D90 or D7000 or better to get AF and easy AE etc.

You will also need to think about the crop factor, cameras up to and including the D300s are all cropped sensor, so your lenses will become in effect, more telephoto, behaving more like a lens 1.5x longer. Great for telephoto reach, not so great for wide angles.

If you want the lenses to behave as the did on your film body then you need a D700 or D3 series FX type camera.