I found myself in exactly the same position about a year ago. Here's the thought process I went through:
1) If it's a marketable idea, one that could make bucketloads of money, the employer is going to pursue it. They'll even want you to spend work hours on it. Or they'll apply other company resources ($$$) to it.
2) If it's something you think is super cool, but isn't marketable, the employer isn't going to care about whether you do it on your own free time.
3) If it's an idea you think is awesome, your employer doesn't agree, and you turn out to be right (it becomes successful), this is the only place where there's a rub. One option (if it's some sort of internet site) is to run it through a proxy (person)--get a friend/neighbor to set up the service but give you all the necessary access to develop/administer it. Another is to fully develop the idea, but hold off on implementing until you're out of the employ of your current employer. A third option is to talk to legal and/or your boss and see if you can carve out an exemption from your contract for work not related to your employer's business.
For my current employer (who has a policy quite similar to yours), they were very open about the reason for such a policy. Simply put, they're hiring you for your mind, and if you've got a great idea, like it or not you'll be thinking about it during work hours. If you feel your current employer isn't compensating you sufficiently for all of the products of your mind, then you probably need to either A) talk to your employer about it, B) find a new job, or C) reassess how valuable your work really is. No offense is intended, but since you haven't mentioned how well you're paid, or even what industry you're working in, I have to leave it as a possibility.