In practice, when I say 有可能, I'm simply saying that it's possible (reasonable, logical) that something happens, but I'm not saying that it should the case.
When I say 可能, I'm saying that it's probably the case. (In daily conversation, you can hear it used a lot to mean I'm afraid..., e.g. 他可能不會在喔。(He probably won't be here=I'm afraid he won't be here.) That is a polite rejection there; you either go for another time or you give up. Otherwise, if they say 他有可能不會在喔。(There's a chance that he may not be here.) You can expect some follow-up confirmation here. They might perhaps run your request by the person you want to meet and check his schedule first and then check with you.)
Skatinginbc seems to say they mean the same, but in my experience, if you replace 你能不能帮我 with 你可能帮我吗, it will cause misunderstanding.
In most contexts, 你能不能帮我 means "can you help me" while 你可能帮我吗 would be a rhetorical question to say "is that even possible for you to help me?"
As I said in post #2, 可能 has multiple meanings, and therefore 你可能幫我嗎 is ambiguous. "你可能(=可以能夠)幫我嗎" in my previous post is meant to specify a situation in which the speaker uses 可能 to mean "can" (可以/能夠). In that case, 你可能幫我嗎 = 你可以/能夠幫我嗎 = 你能不能幫我 "Can you help me?" (e.g., 我想今晚入宮刺殺狗皇帝，只是路徑不熟，不知你可能幫我？). The possibility of such an interpretation is what makes it different from 你有可能幫我嗎, which could only mean "Is it possible for you to help me (either a true question or a rhetoric question, depending on the intonation or context). Of course, if its meaning "in most contexts" (as opposed to its potential difference from 有可能) is what we are discussing here, then 你可能幫我嗎 = 你有可能幫我嗎.
As others have explained, "可能" and "有可能" are used interchangeably in Mandarin. Messquito suggests otherwise, but I think in the examples he gives, whether "可能" means "probably" or "possibly" totally depends on the speaker's tone. Then again, I'm from Beijing, maybe they are different in Mandarin spoken in Taiwan and other places.
"可能" originally meant "may be able" (可=may, 能=able).
The phrase then became a word that can be used as an adjective (possible, probable), an adverb (possibly, probably) or an auxiliary (can, may) depending on context.
Its use as a noun to mean possibility, as in "有可能 (there is possibility)", occurred in modern Chinese. A large amount of foreign literature came into China in the early 20th century following the fall of imperial China. Because the grammar of 汉语 is quite different from most other languages, the practice of using adj., adv. and aux. as nouns, or changing them to nouns (by adding the suffix "性", e.g. 可能性, 可行性, 复杂性, 随意性), became common when translating foreign literature. This is only one of the many influences foreign languages have had on the development of 汉语.
So, "可能" and "有可能" are interchangeable, but "可能" is the original Chinese and "有可能" is Westernised Chinese grammar.