Maybe. Depends upon the camera.
You can use most older Nikon lenses on Canon bodies, for instance, with the right adapter. Most of the mirrorless cameras (Olympus and Panasonic m4/3, Samsung NX, and Sony E/FE) can use Nikon lenses with the right adapter, as well.
But—you knew there was a but coming, right?—there is one thing you need to watch out for. Nikon's older lens designs use a mechanical connection to the camera to adjust the actual aperture. So, with lenses that don't have aperture rings (G-type), mounting them on another camera with an adapter means you're stuck at the smallest aperture. What you need in that case is an adapter that allows you to manually manipulate the lens aperture arm. Such adapters exist, but usually are more expensive and you won't have specific f/stop markings to guide you. Note that with the most recent Nikkors, the E-types, the adapter needs electronic control of the aperture.
Older Nikkors (e.g. D, AI, AI-S), with aperture rings generally work better on other cameras because of the aperture control issue: the aperture ring still works for setting f/stops directly.
One other thing to note: you may be restricted to only certain exposure modes with that other camera, and some—such as most Sony models—need to be set specifically to shoot "without a lens" because no electrical signals are being transmitted through the lens mount as the camera expects with most simple adapters.
Most recently there are a few adapters that claim to control all aspects of the lens (aperture, VR, focus). I’ve had mixed success with these adapters. One early one actually damaged the Sony camera it was mounted to, even though it was a Sony-specific adapter.
So, be careful. Don’t experiment on expensive cameras and lenses.