When I first started I was getting terrible lower back ache and my neck would start to ache from being haunched forward and looking up. It faded after a few months - I adjusted my seat height a bit and maybe those muscles toughened up too. I do still get the occasional ache and pain in my lower back and neck, but I assume that's normal and stopping for a break along my ride helps it to settle.
A new one I'm getting is terrible wrist pain, especially when spending long times on crap roads in city centres where they've been dug up over and over again, so it's not a smooth ride. My wrists seem to take the brunt of it all and can be sore for several days afterwards. I'm thinking of doubling up on my handlebar tape to add some cushioning.