Here are a few suggestions:
1. Take student questions seriously. In my experience, students aren’t born disliking math, and probably everyone is naturally interested in the subject. But once they’re taught that it has no relevance to their lives, and that there are no questions to answer, just insipid “problems” to solve, they learn to hate it. In my experience, the questions students ask are often the most interesting (and historically relevant) anyway. “Is infinity plus one the same as infinity” is actually a deep and mathematically useful question to ask. What does it mean for infinite sets to be “equal” in size? These questions take you interesting places, and if you’re a clever teacher, it’s not hard to take student questions seriously and still cover the curriculum you need to cover.
2. Mention great results and unsolved problems. So many people think that there’s nothing left to do in math. In reality, we know so little it’s shocking. We have a quadratic formula for degree 2 polynomials. We have a cubic formula for degree 3, and a quartic formula for degree 4. Quintic formula? Don’t have one. Ditto for every degree above 5. Is it even possible to find it? No. How do we know? How is it possible to prove anything is impossible without testing all the (infinite) cases?
3. Teach math along with it’s history. Isn’t math more interesting if we learn that the field of probability started with two mathematicians gambling? Or that the person who proved that there can be no quintic (or higher) formula died in a duel, after having written a letter the night before that solved the historic problem and gave birth to three new fields of mathematics?
These are all illustrations of the point which others have already mentioned: if students are invited to have a personal, relevant engagement with a living subject, they’ll find it interesting; if they’re forced to memorize a bunch of rules for no reason that have no usefulness anyway, they’ll find it boring and stupid.
(For more, check out this fluther question about the excellent essay A Mathematician’s Lament.)