Reasonable = ruled by reason, or capable of being reasoned with. When you interact with a reasonable person, you can persuade them to do something an emotional person might not want to do, but appealing to their logic. They're fair. "Talk to your boss about taking the weekend off. You've worked hard, you deserve it. Your boss is reasonable, and he'll understand".
Sensible = reasonable (perhaps), but there's an element of "wisdom" here too. A sensible person doesn't eat too much. A sensible person saves a portion of their earnings. "I got a tax return earlier this year. I'm going to talk to my brother about it. He's sensible, and he'll know the right thing to do with the money." "To invest the money in a mutual fund is a sensible move."
Sane = not insane. Example: "I want to live alone because I can never find a sane roommate. They always turn out to be crazy." "Steve Jobs ate nothing but fruit for more than a year. That doesn't seem sane to me."