Very likely yes. But you'll need the appropriate "adapter" for that. Some camera makers have optional adapters for a wide range of lenses (e.g. Panasonic); some only have adapters for their own (e.g. Nikon, Sony). Fortunately, third party makers like Novoflex have been filling in all the gaps.
But...you need to be aware of a number of things that might arise:
- Automatic features (focus, VR, etc.) aren't likely to work. Exceptions: the Sony Alpha mount adapter for the NEX, the Nikon F-mount adapter for the Nikon 1.
- You may be restricted to certain exposure modes (typically manual exposure mode) and features on the camera.
- You may have to set something on the camera (e.g. "Shoot without lens" setting on some models).
- Manual focus lenses are still manual focus. Different cameras have varying focus aids to help, while some have none.
- You have to be aware of the crop factor: a 50mm lens on most mirrorless cameras is a telephoto, not a normal lens.
- The lenses may be a lot bigger than the camera, especially since they were designed to be used on a deeper camera in the first place, plus the adapter sticks out, too.
- Not all older lenses perform great on newer digital cameras.
That said, many of us use our older lenses quite successfully on our mirrorless cameras.
See this article on adapting lenses.