Usually yes, but it depends on a couple of things.
A modern flat TV screen, plasma or LCD has an aspect ratio of 16:9.
Movies are commonly filmed with an aspect ratio of between 1.85:1 (standard wide-screen, non-anamorphic) to 2.35:1 (CinemaScope or other anamorphic wide-screen processes such as PanaVision 70 or VistaVision).
When movies are transferred to DVD the difference in aspect ratio is treated in one of three ways.
The one preferred by most movie enthusiasts is called letterboxing. In this method the original picture format and framing is retained and the image is positioned to fill as much of the screen as possible. The remaining, unused area is blanked. For older TV programs and early movies the blanking will be on each side of the image. For wide-screen movies the blanking will be on top or bottom. Often these will be a very small bands and after a few minutes not really noticeable.
In the second method the original image is cropped to fit the TV screen. The disadvantage of this is that part of the image the director and cinematographer carefully composed is lost. In the worst cases this can result in characters being cut off and dialog becoming disembodied.
The third method is a variation. The image is still cropped to fill the TV screen but the frame is panned as the film is scanned to keep essential action and characters in frame as far as possible.
The simple answer is that, yes, wide-screen DVDs will fill your screen -- one way or another.