not if your settings state that your account is only visable to your friends. they don't get notified either, but they might notice when the 'people you might know' tool suggests you to them again! (no biggy)
if you click settings in the top right and then privacy settings. At the bottom of that page you can block people. If you block somebody they can't see anything you do or any of your profile no mater what.
...in addition to what sara3 says, if you tag your ex-friend in a photo, you can actually set your account to stop them viewing the rest of the album that they're not tagged in (for each album change to "only my friends")
if you don't want to go to the extremes of binning them off, you can exclude them from viewing what ever you want (settings > privacy > profile then select 'customize' under each category). ideal for if you're friends with an employee, a relative or your employer!!