I believe you need to be more precise about "spare time". Another issue might be "spare resources."
I believe it's the case (and law(?)) that in many places, if you don't sign a contract explicitly granting you the rights to your "off hours" work, than any work you do that uses any of your employers resources (the offices, the computers on site, the computers that he has loaned you that you have in your home office, the DSL line that the employer picks up the tab for, etc.) can be construed as the property of your employer. If you do plan on working on your own time and for yourself while employed, you should consider using all your own resources, including connectivity. And that's almost getting to be common practice these days, I know of many people with two lines into their home. One paid from corporate, the other paid for from their own pocketbook. Ditto with email of course. Make sure all your own work is clearly separable from what your employer is paying you to do.
As David suggests, it's better to let your employer know that you intend to work on non-competitive projects in your spare time. (Perhaps in your written acceptance of their offer?). Best if you can get them to sign a contract granting you rights back to your own time. What a crazy f'n world, eh?
This crops up on /. periodically, and though few of them are lawyers, you might get some wider views what to expect and what to do there.
