These 3 words are largely interchangeable.
To the question: "Is there life on Mars?", for example, "Perhaps", "Maybe", or "There might ( be) " are all equivalent answers.
To the question: "Are you going to the movies tomorrow night?", "Perhaps" and "Maybe" are equally valid answers (indicate the person is undecided). "I might " suggests the answer is dependent on something else (e.g. "I might be, if my cousin doesn't visit").
If someone is asking about WHETHER I'm going, "I might be" is the better answer.