When I was in the Academy I got rides in a UH-1 (Huey), an HH-60 on a live fire exercise (even got a chance to shoot the .50 Cal on NVG's), an MC-130 and an AC-130 as part of one of those dedicated Academy/ROTC programs (called "Ops Air Force").  
     As an officer, I've only had a chance to fly on C-5's as a space-A passenger, and in the back seat of an F-15D out at Kadena.  For the F-15 ride, I was already a pilot on KC-135's so all I needed was seat training (which took all of 15 minutes), and since I was a rated pilot, a lot of the restrictions that are normally placed on the mission didn't apply (so we could do any training mission, we could look at classified, we could go above 18K, etc., etc.)
 
     As the pilot giving the incentive ride, I've had JROTC cadets on the KC-135 a bunch of times.  We used to take up about 10-20 JROTC guys at a time as long as we had 1 extra crew member to act as a passenger monitor, and then we'd let 2 in the cockpit for takeoff and 2 for landing (since that's how many extra seats we had).  We'd also let them cycle through during the air refueling in the boom pod, so everyone got a chance to see the F-15 or C-17 or whatever pull up and get his gas.  
 
     As a tweet pilot, the only guys I've taken up who weren't student pilots were ROTC and JROTC cadets, and I took up 1 USMC gunnery seargeant who had won some kind of award.   On those sorties we would always go up single ship, but we were pretty unlimited as to what we could do aerobatically.... so loops, rolls, cloverleafs, and cuban-8's were all acceptable- until the kid pukes.  
 
     A buddy of mine was even able to work out a deal with the squadron commander and the public affairs office to fly "The Fray" (the guys who sing "Cable Car" and a few other songs).  Apparently he knew the guys from high school, and he was able to put together two 2-ship formations, so those guys got to go up in formation.  Of course after the flight they put on a concert in the local area and offered everyone from base reduced price tickets!  
 
See here: 
http://www.justgetfit.com/The Fray.htm  or here: 
http://www.columbus.af.mil/news/story.asp?id=123039425