Will my Nikon D70 lenses work with the D300?

Yes, any lens the worked with your D70 should work fine on your D300 since they’re both DX format cameras.

The D300 is NOT a full frame camera. (The D700, D3, D3x, and D3s) are the only full frame Nikon DSLRs.

Thank you! That is very useful. As a follow-up, if I WERE to buy a full frame camera, what changes would I see in my photographs if I used these lenses?

Any DX lens will work on a full frame camera. However, the camera will automatically crop and use the center of the sensor for those lenses. This results in a decreased resolution of about 6mp. There may be some other problems such as vignetting in your photos.

Generally, it’s recommended to stick with full frame lenses to avoid these problems. (Heck, if you’re willing spend the money on a full frame Nikon DSLR, you might as well spend some more on the lenses right? :D)