To me, adding 'up' suggests completing the job. Cleaning is more general - you could be doing a little, or doing a lot. There is no more information. 'Cleaning up' suggests you are finishing the job. If you have 'cleaned up' the kitchen, I would assume that it is now completely clean. Michael gave an equivalent example of ripping - where ripping up means complete destruction. If you beat someone up, you leave them completely beaten, whereas in the case where some parents beat their children, it is obviously not usually that extreme a beating. In other cases, such as 'wash', it is less distinct a difference.

Hard question to answer. If I say, "I am going to clean," it means the same thing as, "I'm going to clean up." It's mostly a colloquial thing. In some ways, adding the word "up" might imply a general and broad application of the action. I'm going to "clean up" probably means you're making your whole house clean, where saying I'm "cleaning" might lead to the question, "What? What are you cleaning?" In the same way, saying, "I'm ripping the paper," kind of implies a single or partial rip, where saying, "I'm ripping up the paper," means you're ripping it to shreds -- destroying it. But if you just ignore the words "up" you won't be missing any meaning. It's mostly a meaningless addition to verbs.

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