What matteres is not the manufacturer of a lens, but its lens mount. In fact, there are two things that have to be considered.

First and most important aspect is probably the flange focal distance. This is the distance from the mounting flange (the metal ring on the camera and the rear of the lens) to the film plane.
In order to achieve infinit focus, this distance is essential. Every lens mount has a different one. Look at this list for reference. To be able to focus to infinity, the adapted lens has to have the same flange focal distance as the mount dictates.
Let's look at an example:

• Say you want to put a Nikon F-Mount lens on to your Canon EOS M. No problem at all! The Nikon lens is made for a flange focal distance of 46.50 mm. The Canon EF-M-mount has a distance of only 18mm. This means that you need an adapter that adds additional 28.5mm between lens and sensor.
• Another one: You have a old Leica M39 lens, that you want to put on your D3200. The lens is made for a flange distance of 28.80mm, where the D3200 sports 46.50mm. That means that the lens is at least 17.7mm too short (not counted the addtional space that a adapter adds). In this case, the only thing you could probably do with that combination, is macro photography.

Like mentioned, if you look at the linked table, don't forget, that an adapter adds some extra millimeters space.

Another thing to look out for is the mount diameter. If the diameter of the mount of the lens is larger than the diameter of the camera mount, the adapter has to be put entirely in front of the camera, adding some extra flange focal space.

That said, there is a workaround, when adapting lenses with a small flange focal distance on a camera with a larger one:
There are adapters with a corrective lens built in, like this M42-to-Nikon F-Mount adapter from Kipon. That built in corrective lens tries to make up for the difference in flange distance.
However, as this adds another glass element (and most adapters are too cheap that they could possibly be of higher quality glass), there is a high propability that this affects image quality negatively.

Second aspect to think about, is the built in electronics.
If you adapt a old lens to your camera, you will most likely end up with complete manual control of your exposure and focus. Old lenses had no auto-focus, and no transmitting of exposure settings, like aperture.
Higher end cameras, like the Nikon D800 are able to measure the exposure and so work at least in aperture priority mode, setting the shutter speed automatically, addtional to the manual mode. Entry level cameras like the D3200 can't do that with non-CPU lenses and have to be operated fully manual, as they can't determine that a lens is put on without the CPU.