Is it possible to control aperture while using a mount-adapter and lens which does not have an aperture-ring?
Yes, but if you're not using an adapter that does electronic communication between the body and lens, it's a serious pain-in-the-butt. I've heard of it working the same way on both Canon and Olympus, so I'm assuming it may work on more than just those two systems, but you essentially mount the lens on a native body that does communicate with it, then you hit a DoF preview button, and unmount the lens while it's stopped down. Then adapt it.
And you have to do that every time you want to adjust the aperture. It's not particularly practical, but can work.
The easiest thing to do would be to get an adapter that supports electronic communication.
If so, for which combination of lens mounts is this possible?
Mostly the "smart" adapters have been for Canon EOS lenses (since Nikon only recently removed aperture rings with the G-series lenses, but Canon lost 'em back in the '80s) to the micro four-thirds, Sony E, and Fuji X mounts.
Are there specific models which support this?
Metabones is probably the best known maker of adapter rings that provide electronic communication when adapting to mirrorless, but with the full mount communication, they do also provide aperture control from the body. Most notably for Canon EOS to Sony E, Fuji X, or micro four-thirds (common usage pattern for some folks moving to mirrorless).
There are also adapters that come with their own aperture iris, but results can vary since the iris not being where the optical design expects it to be can introduce flare.
There are also some mounts (such as Nikon F), where the adapter ring can take advantage of an external aperture lever to control the aperture on the lens from the adapter ring. This is likely to perform better than an adapter with its own iris.