Should you use a tripod? It's entirely up to you. The rule of thumb for shutter speed that Alex describes is correct for film cameras or full frame dSLR. For dSLRs with smaller sensors such as your Nikon, the rule of thumb should be adjusted by the crop factor of the sensor (I'm not going to argue about this, if anyone disagrees then search the forum for a very good explanation of why this is so). Given this adjustment for a 28mm lens, the normal figure would be 1/30th but this becomes 30x1.5=roughly 1/50th on your camera. If you have some form of image stabilisation then you should be able to get about 2 stops better than this.
However, this is only a rule of thumb, some people are much better at hand holding than others. Mrs. Y has been known to get acceptable results at 1/15th second with a 200mm lens, on a 1.5x crop factor camera with no image stabilisation!
Personally, I think if you're serious about landscape photography then this discussion should not be happening. Apart from giving you complete freedom w.r.t. shutter speed and ISO, using a tripod slows your thought process down, makes you think, gives you time to really see what is there in the viewfinder. It makes you frame the shot up with a more considered opinion, makes you work at getting the composition right, or at least a lot better.
Using a tripod will make you a better photographer regardless of the shutter speed you end up using. It stops you "snapping" and makes you take photographs.
Duncan
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