I just came back from a T-37 and T-6 assignment, and I'm in the KC-135 now. As for hours per year go, it's kind of a question of how you define "lots." It may be a "lot" compared to other airframes in the military, and it is DEFINITELY a lot compared to guys who are paying out of pocket to fly GA (unless they are just filthy stinkin' rich and flying their butts off!) It's probably more than a CFI flies, but that is just a guess. Compared to most of the regionals or the majors, it's probably a lot less.
In my career, 300-400 hours per year has been about average. In the training commands you can go cross country just about every weekend if you want to. Generally, the guys who do are young and single... but even then you do get burned out on that pretty quickly, and guys wind up settling into a pattern where they go out maybe one weekend a month (if they like going a lot) or about 1 weekend every 2-3 months if they don't. Some guys have girlfriends in other towns and so they are gone as often as they can... to get some "recurrency training." Others have a girlfriend or wife at home, and they just don't want to leave that often. So while it seems like all the new guys to the T-37/T-6 world begin with a 600-700 hr/year rate for about the first 3 months, it's hard to keep that up and there really is not a reason too. It'll drive you crazy! They generally settle down to that same 300-400 number... probably closer to the 400 end.
As for the -135, again, that depends. If you deploy to the desert a lot you may see as much as 600-700 hours/year... but again it seems like most guys settle in at around the 300-400 hour/ year range. There are always other things that come up and get in the way: staff jobs, a deployment as a planner, a professional conference, you get picked to be on a safety investigation, you get picked to be the life-support officer and have to go to a school for a couple of months, you become a Chief of Training and there is an inspection coming up, you get a longer term injury playing sports, you get picked to be the executive officer and the squadron commander won't let you go on any trip longer than a week any more or he'll only let you fly Tuesdays and Thursdays, you become the representative for this year's airshow, etc., etc. There are a thousand things out there that get in the way of just flying every day. They are all important, both to the military and to your career as a professional military officer. But they do limit the flying.
Now, that is officer specific, and Air Force specific. My general sense is that for the Navy and Marines the story is similar, from talking to those guys, but you'd have to ask them for better data. I've heard that for the Army it is even worse for the officers, who almost never fly, because the lion's share of the flying is done by the warrant officers. So for an Army officer, my guess is that 300 hrs/year would be a HUGE year for them. IanJ would probably know better.
Now, I've heard that my airline buddies fly something like 70 hours a month, or 75 hours a month, and if you figure that that works out to about 800-900 hours a year even the "burnout rate" of 600-700 hours that no one seems to be able to achieve long term in the Air Force is significantly less than that. Of course, I've heard some "alibi's" on their numbers also: some months you just sit reserve and don't get called that much, that number is a maximum, it's not really a guarantee, you may get furloughed and not fly for a while, etc., etc. Maybe some airline guys can talk about their work schedule a little more to put it in perspective.
To sum it up: a "lot" is really a question of perspective. A "lot" compared to who?