May and might

Using may and might is another way to talk about possible activities or happenings in the future:

• I'm not sure I'll go to the party. I may be away.
• Don't drop by at 7.20. I might be watching TV.
• Prepare something to eat. Mr. Johnson might be hungry.
• We may not be able to go to school this week

There isn't much difference between the two. So you can say:

• John might be at home or John may be at home.
• I may visit Mary or I might visit Mary.

 However, when the situation is  not real only might can be used:

• If I were a bit smarter, I might go to college. (The speaker won't become smarter, so the situation is not real)

If you want to emphasize progression of a situation, you may use the continuous form of may/might. Actually you can see an example above:

• Don't drop by at 7.20. I might /might be watching TV.

If you're using the reported speech, may become might.

• "I may be late," said Frank. REPORTED SPEECH: Frank said that he might be late.

Read about Modals in the Reported Speech.