I agree with CF - there are, as he rightly says, 3 ways to delete (highlight song(s), press delete key, choose delete from right click menu, or choose delete from Edit menu) - I personally have used iTunes on several hundred (not an exaggeration) machines (PC and Mac), and it always works as he describes - I have trouble thinking of a situation in which it wouldn't work, but could find a few (e.g. trying to delete something currently playing, trying to delete something on a read-only disk).
In order to resolve your problem, could you please give a bit more information - is it a Mac or PC? If PC (I assume it is - Macs rarely have problems) - is it XP, Vista, etc.
What version of iTunes?
Does the song change colour when you click on it?
When you say it won't delete, do you get an error message?
If you select the Edit menu, is the Delete option greyed out or bright?
Have you been able to delete in the past, but now can't?, or has it always been like this?
I'm sorry if you find this level of detail pedantic and painful, but if you want a definitive answer from someone who's competent, then it's necessary.