C-17s:
1. Ops tempo's varied wildly over the life of the program. Before my time, it was common for guys to be gone at least 250 days a year, but it's not nearly that bad anymore. These days, you can probably expect about one 90-day deployment every 18 months or so, and an average of one 7-10 day mission per month out of home station. As a young guy, you'll also spend a lot of time back at the schoolhouse at Altus. It takes five trips there to go from UPT grad to C-17 airdrop IP.
2. Lifestyle/family stability: highly related to #1. We generally don't get many long deployments, but you'll often be gone for relatively short bursts. Like Jarhead said, it's AMC.
3. Morale: Probably average compared to USAF flying squadrons as a whole. You'll get some amazing opportunities to travel to some really cool places. I've been handed papers before to fly to a country I didn't even know existed at the time (Mauritius, as an example). But the sweet trips are tempered with the usual AF BS. Most C-17 guys who are past their UPT commitments are now based at KATL or KJFK, leaving a relatively young and inexperienced crew force behind to pick up the slack. Like I said, standard.
4. This jet's not going anywhere. Being a newer airframe, she's already got most of the bells and whistles that you want. The jet was designed with a 30,000 hour service life in mind, but several of the tails have already hit 20,000+. That lifespan will be extended well past 30,000 in due time. As far as usage goes, I don't see any real changes coming down the pipe. Wherever the US gov operates, which is everywhere, there's going to be a need for airlift.
5. Besides the FTU at beautiful Altus, there are seven AD C-17 bases: four on the west coast (McChord, Travis, Elmo, and Hickam) and three on the east coast (Charleston, Dover, and McGuire). Charleston and McChord are by far the two largest hubs, each with close to 50 of the 223 tails. There are also some limited opportunities to pick up exchange tours with the Aussies, Brits, or Canadians or to go out to fly with the HAW, a NATO unit based in Hungary.
All in all, I've really enjoyed it. If you like to travel and you like working with a team of guys and gals on a crew airplane, you'll have a good time. The mission set is varied enough that it's never the same thing twice. You'll see plenty of Iraq and Afghanistan, but you'll also wake up in Peru, Chad, Myanmar, or wherever else Uncle Sam wants to go that day. Pretty fun gig.