I'm with those who get into their tanks barehanded as little as possible. As I see things:
1. Your hands and arms are rife with bacteria, viruses, dead skin, hair, oils, and who knows what else unless you scrub them thoroughly with soap and water.
2. You do not want to put your hands into the tank water after washing with soap and water no matter how well you rinse them. Almost all soaps contain lingering perfumes and chemicals that rinsing does not easily remove.
3. Washing with just water really isn't washing. It's just rinsing off some of the bigger junk. Better than nothing, but still not so good.
4. An open cut could indeed lead to a very serious infection. Even if rare, that's a serious and unnecessary risk.
5. Yeah, some people at my LFS do this, too. But they do it all day long, so their hands are constantly rinsed in tank water.
Your local farm supply store sells shoulder-length, disposable/recyclable polyethylene livestock exam gloves that provide decent protection for both yourself and your tank water. They'll fit over long-sleeve shirtsleeves so you don't need to change clothes or roll up your sleeves before getting into the tank. I buy them in a box of 100, so they're typically about $.10-.15 each. They're sometimes sold as "OB Exam Sleeves", so even city folks will probably get the idea of their intended purpose.