My experience was surprisingly mundane. Most all of my rides were at least a little weird in some way, but most people just want someone to talk to. I only remember a couple of rides in particular that asked me questions or tried to get me to tell stories. And people know they'll never see you again, so many won't hesitate to confess some weird shit. The only sketchy ride I had was a guy that had been drinking in Kentucky, and even that wasn't too bad until he started drinking again while driving, at which point I asked him to let me out at the next exit. If you hitch only in the daylight and stick to interstate on-ramps, I don't think it's too dangerous. I'm also a tall, well-built guy, too, so of course YMMV. I'd definitely recommend trying it, though.
It was harder to get rides in the east than it was in the west, but even then I don't remember waiting much longer than an hour anywhere for a ride.
It was an awesome experience overall, but I was worn down by the end of my trip, and I don't plan on hitchhiking again. I'd say go for it and try it, though.