If your in Norway for just a weekend, you will most likely only get to see Oslo. Or at best take in the Norway in a nutshell tour (round trip bus, train, boat trip from Oslo to Bergan) that takes in a lot of the postcard scenery.
If your here longer there are plenty of sights to see, only problem is everywhere requires a lot of driving to get to.
On the west coast you can see
Prekistolen (located near stavanger) 2 hour hike to the top..
http://www.preikestolen.no/
Bergen - Nice town on west coast.
http://www.visitbergen.com/default.asp?sp=NO
Trollsteigen, road that winds down mountain
Gerianger fjord (located between bergen and trondheim) .. post card fjord
East
Oslo - Frogner park, nobel peace prize museum, ski jump, frognerseteren, arker brygre.
www.visitoslo.no,
www.norway.com
South
The south is nice too, its more sea side towns though, not the kind of thing norway is known for..
North
Lofoten (near bødo) -- , Tromso...
Its very expensive but if you avoid eating and drinking out, and travel off season you can get some good deals