There's no single answer to this. My experiences as a C-17 guy from 1998-2009 will be a lot different than a new C-17 pilot today. But I averaged about 350 hours per year. The first year was only about 150 hours, but then things picked up. Some years were closer to 500 hours with up to 170 hours in a single month.

On average, I'd say that a C-17 pilot will fly about 3-4 hours in the sim per month, about 1 or 2 locals per month (about 5 hours per local, but time is split between several pilots), and a hugely wide variety of operational flying, but probably average about 30 hours per month.

At about the 5 year point, you will start flying less - instead of 1-2 overseas trips per month, you might get 1 per quarter.

I'm at the 13ish year point and I've been doing non-flying work since the summer of 2009. It'll likely be 3-5 years before I'm back in the cockpit.

Realize that different airplanes have vastly different flying schedules.
C-17s and C-5s generally fly locals and 7-14 day overseas trips (about 30-50 hours per trip). C-17s will also deploy as a flying squadron for about 4 months and you'll probably fly your butt off. C-5s don't do flying deployments.

Everyone is vulnerable for non-flying deployments. Everyone is also somewhat vulnerable to getting assigned to fly UAVs (aka RPAs), which the AF counts as a "flying" assignment.

C-130s, KC-10s, and KC-135s generally fly locals and 4 month deployments. Not sure about the ability to fly shorter overseas trips - probably not as many of the short trips as the C-5s and C-17s do. I think some of those units break their deployments into 60 or 90 day chunks of time.

Fighters and bombers generally fly locals and Red Flag (or similar) exercises and 4 month deployments.

I'm sure that some of these other folks will chime in.