I would recommend cameras with 4/3 or APS-C sensor sizes. Even with micro 4/3 you need a 16MP sensor, and it has to be a Sony sensor, which specifically limits you to Olympus for a compact camera. Sony also makes the sensors for Nikon, Sony, and Pentax cameras so they are good choices as well, with slightly larger sensors and proportionally larger cameras and lenses. Fuji also makes nice large sensor cameras.
You will also want a wide aperture, wide angle lens. Wide aperture helps because the wider the aperture the more light hits your sensor, resulting in a less noisy image. It will also give you more leeway to adjust shutter speed and ISO. I wrote about how to get lower noise in a thread a few months ago, about ten threads down. The lens needs at least f/3.5, but preferably f/2.0 or larger (i.e. lower f/ numbers). The wider the lens angle, the more flexibility you have in apertures.
Wide angle helps to keep the star trails from getting too long, because they cover proportionally less distance in 60s across a lens with 120 degree field of view than a lens with 60 degrees (which doesn't matter for star trails). Wider angle also allows you to get more of the foreground in focus at a given aperture.
Here is a composite time-lapse image with Olympus E-M5 and Rokinon f/3.5 7.5mm fisheye. You could get the same result with the more compact Olympus E-PM2 camera, which has the same sensor.
Here is another with Olympus E-M5 and f/2.0 12mm lens. You could use the Panasonic f/2.5 14mm lens for a almost decent, nearly wide aperture lens, with almost as wide a view that is much cheaper and lighter. (However I sold mine for the 12mm with no regrets.)
If you are away from city lights night images are more difficult. I think you would, for example, be hard pressed to get a new-moon star trail image from Desolation Wilderness with a LX-7. In fact from my perspective it would be impossible. If interchangeable lens cameras are too large/complicated, there are some good fixed lens APS-C cameras about.
A couple additions: Notice the images above me were shot in full moons, bright city lights, or at twilight. Trying to get an image when only star light is present is harder and would generally require a larger sensor (4/3's or larger). Another note, I take star trail time lapse images by placing rubber bands around my camera's shutter button when it is in continuous shooting mode (they have a day job of holding my tent stakes together).