A friend of mine and I were discussing phrases like "artsy fartsy" and "hoity toity" and wondering a) if that sort of rhyming phrase had a name, and b) if there were more of them that we didn't know about. I should have known the answers were available on the Web. Words like that are called reduplicates and some of my favorites (found here, scroll down to the bottom) include dilly-dally, fuddy-duddy, higgledy piggledy, hurly-burly, and namby-pamby.
Related to reduplicates is Cockney rhyming slang, one of my favorite "features" of the English language. I'd start using it in daily conversation, but I fear that no one would know what the hell I was talking about, which, according to the explanation of what Cockney rhyming slang is, was probably the point.