A tripod is an important component in any serious photographers set up, not just an accessory.
The following playlist is a few reviews of cheap tripods. Only a few reviews so far but that will grow over time.
One of the main reasons for using a tripod is to avoid camera shake and maximizing your image quality. When there is no need to raise the ISO or shutter speed and choosing a higher aperture to maintain this image quality, using a tripod would definitely improve your photography. Many lenses today have built in optical stabilization (which is handy in certain public areas where there may be restrictions on use of tripods) however there is no substitute for a good quality sturdy tripod when time is on your side for that professional looking image.
For landscapes where you want sharp depth of field and or that silky motion of water effect with slow shutter speeds then you must use a tripod to achieve this (remember to use your remote cable or timer). If you feel constricted using a tripod composing your shot before attaching the camera to it may be easier for you. Tripods give you that control not only for shooting landscapes but for portraits, products etc on location and in studio.
This is a video review of the Slik s640 tripod for beginners.