I take out my hay for the week from the equipment bay or the loft, and stack it in a small space I designed specifically for this purpose. It is a long, but narrow area between a stall and the tack room so I can stack up hay pretty high. I have gone as far as throwing 6 bales high, but generally I stop at 4. I admit that beyond 4, it gets harder to throw them up there, but I can do it if I have to. I'm about 5' and 115 lbs, and I've noticed that I've gotten a lot stronger since having horses at home.
When we pick up our hay for the winter (we usually do it in several separate loads), I prefer to toss them off the wagon onto the truck and trailer and let my husband stack them up high though. Throwing them over my head is a bit too hard on my back.