In general there is little difference most of the time! However, there ARE differences. Please give me a minute to make a nice cup of coffee... and then I'll explain.

REPORTED SPEECH: We often backshift present to past so, "It MAY rain," would usually be reported as, "She said it MIGHT rain." However, it would not be wrong to say, "She said that it may rain." Especially if the reporting were nearly contemporaneous. TO SHOW ANNOYANCE/FRUSTRATION: "Well, you MIGHT have told me you were not coming! Huh! I cooked dinner. What a waste of food!" "People MIGHT try to be more considerate! Tut!" You need to sound really quite annoyed for this to work well! (MAY does NOT work in this situation) To be VERY POLITE: Try MIGHT! "Might I borrow your pen?" (Rather formal, very polite, a bit old-fashioned perhaps) MAY is also polite. "May I use your phone?" CAN works here, and is probably the most common form, but some people find it rude, and some consider it incorrect usage. "Can I borrow your book?" "Can I climb this mountain?" has 2 meanings. Do I have the ability? Or... do I have permission? If we keep MAY for permission, and CAN for ability we have regained clarity! Ah! But too late! Everybody now uses CAN for permission so we have confusion! Let's go back to: "May I climb this mountain or is it off-limits?" (permission) "Can I climb this mountain? Yes! I can. And I will! I'm fit and well-trained, so I can!!!!" (ability) HOPES/WISHES/wishing someone good luck You need the word MAY for this. "May you be very happy in your new job!" "May the force be with you!"(Star Wars!) MIGHT does NOT work here. MAY you have a happy time studying MIGHT and MAY! (Oh and don't forget MIGHT also has the meaning of power and strength, and MAY is also a month, and a type of tree... so there MIGHT/MAY be plenty of opportunities where you MIGHT/MAY get confused!)

Section 2. WHERE THERE ARE DIFFERENCES! 1. MAY HAVE / MIGHT HAVE You can use both if you are guessing about a possible result: "I think the President MAY/MIGHT have made a mistake in sending in the troops!" (But you are not sure) If you are referring to a possible result BUT YOU KNOW IT DIDN'T ACTUALLY HAPPEN then only MIGHT sounds right. "The children got across the busy road safely, but they MIGHT have been killed! That road is dangerous!" 2. Degrees of POSSIBILITY. Some people feel, and teach, that MAY suggests something is more likely than 'might' does. I DO NOT AGREE that it is that simple! Only in some cases do I feel any difference. I would suggest A STUDENT uses MAY for more likely things, and MIGHT for less likely things. But remember that native speakers will often not notice any difference. It MAY/MIGHT rain tonight so I'll take my umbrella. (What's the difference? To me, NONE!) We can MAKE either word sound more or less possible by the WAY we say it. If I emphasize the MAY and shake my head a bit I can make it sound VERY UNLIKELY that it will rain. "Well, it MAY rain tonight but I really don't think it will so I won't take my umbrella." Or I can make MIGHT sound rather LIKELY - "Dear me! It might rain tonight. They said so on the weather forecast. I'd better take my umbrella!" WHERE I FEEL THERE IS A DIFFERENCE: If you really are making a guess, and you are full of doubts, then I think MIGHT does work better. "I don't know how old he is. I'm not good with ages. He LOOKS as if he MIGHT be about fifty. But he could be forty or sixty! I really don't know." In hypothetical situations MIGHT is definitely preferable. If I were rich, I MIGHT buy a yacht. (MAY really does not work here. The 2nd conditional really needs that past form - might) However, with something a little more likely both work. "If I get that promotion, I MAY/ MIGHT buy a new car." Another cup of coffee needed before Section 3!

The verb MAY is used in 5 main ways: 1. Possibility. "The rumours MAY be wrong." (or they may not) 2. Polite request TO someone/permission. "May I go now?" 3. Polite permission FROM someone. "You MAY go now." 4. Admission of a fact before stating a contrasting fact. "He MAY be short but nobody can play basketball better!" 5. To express a wish or hope. "May your marriage be happy and long!" Basically MIGHT is a past form of MAY - HOWEVER it is NOT always USED as a past form!!! Examples: He MAY/MIGHT come tonight. (future use of both) Oh dear! I MAY/MIGHT have lost my keys. I can't find them anywhere! Help!" (present/past meaning) He MAY/MIGHT have gone home at lunchtime. He was not well. (past meaning of both) The general rule is that they are INTERCHANGEABLE. There MAY/MIGHT be a slight change in meaning, but often there is not. In the next section (in the next answer) I will try to explain where there ARE definite differences.

'May' is used when we talk about the present / current situation. 'Might' is used when we talk about something that happened in the past.