In the car a while ago I thought of a good exercise to help you guage your pitch accuracy.....Two actually.
One play a note on the piano (guitar, recorder, whatever) think the pitch and sing it back.
Once you've got that down think of a pitch in your head and match it. This variation will improve your ability as a musician by far.
I often think I would like to try to revive jazz vocals and put a big emphasis on improv vocals. This kind of exercise will help you do that. The best guitar players, bass players, etc, can all "hear the pitch in their head" before they play it and singing should be the same way. If you can anticipate a change then you can sing anything in an instant and sing it on pitch, too. No one would be the wiser.
Normally I'd say do this exercise after you have a full understanding of your voice and its limitations...but I think you're ready for it.
One thing I like to do (in the shower, car, wherever I won't embarass myself) is pick a style and ad lib a song to it. Usually works best with an easy listening style. This is actually more difficult than it sounds because if you do it right you end up exploring alot of very unique melodies involving altered pitches. Its great fun.