Here's a slightly different take on the problem.
It's exactly the same as Jason's suggestion except the correct answer has been put in the questions table. This sollution obviously cannot work when questions with multiple correct answer's are possible. In terms of performance, it would at first appear a bad sollution as you'd always have to join to the questions table, even when you don't specifically need the question. It turns out, however, that you can often factor the answers table out of the query and because the answers table is inherently larger than the questions table (in terms of cardinality) the join should be quicker.
Here are a couple of examples to illustrate the difference between the two sollutions.
Fetching users who got question one correct
# sollution 1
SELECT users.username
FROM users, user_answers, answers
WHERE users.id=user_answers.user AND user_answers.answer=answers.id
AND answers.correct=1 AND answers.question=1
# sollution 2
SELECT users.username
FROM users, user_answers, questions
WHERE users.id=user_answers.user AND user_answers.answer=questions.correct_answer
AND questions.id=1
Fetching questions and the number of users who got them right
# sollution 1
SELECT questions.question, count(user_answers.id)
FROM questions, answers, user_answers
WHERE questions.id=answers.question AND answers.id=user_answers.answer
AND answers.correct=1
# sollution 2
SELECT question.question, count(user_answers.id)
FROM questions, user_answers
WHERE questions.correct_answer=user_answers.answer
