Although any camera can be used to take landscape shots, there are a few features found on some compacts which make them good for shooting landscapes with.
Good Zoom Lens
A compact that has a zoom with a wide-angle of coverage will mean you can shoot a variety of landscape shots. The Ricoh HZ15, for example, features a 15-times zoom lens covering focal lengths from 24mm wide-angle to 360mm super-telephoto (in the 35mm format). This means wide shots of vistas as well as landscapes that pick out detail in the scene, such as a particular tree or building, can be captured.
If you don't always want to work with a tripod, although it is recommended, you'll find shake reduction to be a useful feature. It'll help the photographer take blur-free images in situations which can be prone to camera shake such as at sunset when less light means longer exposure times are often needed.
We know a tough camera body that's water-. freeze- and shock proof / resistant won't help you take better photos but it will protect your gear. This becomes even more useful in winter when cold temperatures set in which can drain batteries quicker and slow the performance of cameras down. Using a tough compact, such as the Pentax WG-3, also means you can take landscapes with a slightly different twist, such as holding the camera half in and out of the sea, and you won't have to dash for cover if it starts raining either (just remember to wipe the lens so drops don't spoil your shot).
A large LCD screen makes it easier to view images on playback so you can check to ensure your shot is sharp. It also makes menus easier to read, making the selection of specific controls more efficient. Some compacts, such as the WG-3, feature an anti-reflection coating on the LCD screen to minimise glare and reflections to ensure an image can be viewed clearly when working in sunlight.
A compact with a tilting screen, such as the MX-1, allows the photographer to adjust the monitor up and down and set it at the angle easiest for viewing. Again, this is useful in situations where bright light levels may stop you viewing what's on screen when in a particular position. It also makes it easier to take shots from different angles such as lower to the ground or up high if you want to make more of a feature out of the sky.
This feature allows you to take control over the exposure in situations where the camera's automatic exposure control may be fooled by a scene that has large dark or light sections. For example, photographing a highly reflective snow-filled landscape would make the camera produce an image which is far too dark as it sees the scene as looking overly bright. The function is also useful when you want to produce an image that has a better dynamic range, something which is produced by combining multiple shots of the same scene in your chosen editing software.
A Scene Mode found on most digital compacts is Panorama and it works particularly well with landscape shots. The beauty with this mode is that the camera automatically stitches shots you've taken together; meaning you don't have to spend time combining images manually in photo editing software. You just have to capture the scene in-front of you, moving the camera left or right in one movement, and the camera does the rest.