There may be more, but this is all I could dig up?
Remember, success does not always have to be measured in terms of national championships. Most of the Vols athletics programs compete on a national level every year. The elite programs at Tennessee are Lady Vols basketball, Track and Field, and Football. The tennis program and swimming/diving also excels. The Baseball team has also had some moments in recent history.
I am sure other people can contribute to this thread with more knowledge on the success of the many programs at UT.