I usually try to schedule my ride and driving days to work so that I don't have to carry anything with me on the bike. Every now and then I might be caught wanting to ride without having clothes at work, and so then I have to take a small backpack, which I really hate. It feels like it restricts my movement too much, and of course the back sweat issue.
I always use my road bike, because my MTB is just terrible for commuting, even with road tires and a rigid fork. Neither bike has rack provisions. I'm considering a beam rack and trunk bag to use some days, but I've read a few posts here saying that it can sway and make bike handling a bit finnicky. I would also have to swap my current carbon seat post for an aluminum post, which I'm not really crazy about either. I love the comfort that the CF post provides.