Remember when the Clinton staffers were about to leave the White House? They ceremoniously removed all of the "W" keys from the keyboards! Fortunately, most people who leave a job don't go around tampering with keyboards although I've seen two who filled up their Nalgene with company water before hopping into the car.
To all bosses- be reasonable. People leave, it's part of work. They may have found something closer to home, closer to their heart or just plain better. While I wouldn't tolerate an employee who bags it with a month to go, it's not fair to withhold pay if one "t" isn't crossed with a day to go.
Understand that the person is looking out for him/herself and trying to make the best decision. It's probably not the beginning of a smear campaign or an attempt to sell all company secrets to the competition. They just plain found something better. Being a gracious boss, even when on the short end of the stick, is still a virtue in my book.
To all employees- communicate your needs before you have to look elsewhere. My theory is simple- if disgruntled employees had an open line of communication with their boss about their future plans, dreams and ambitions, they would be less likely to leave. This of course relies on a boss who has enough self image to have that kind of conversation. Not easy at all but crucial to limiting turnover.
The fact is that replacing you is costly and will set your company back to some degree. Your boss wants you to be happy and if he/she can find some wrinkle to iron out, they'll probably do so. If not, then by all means start shopping. Be smart and plan accordingly but keep working nonetheless.
A personal note on leaving. I've left several workplaces, moving on for various reasons that I thought made sense. Looking back, I probably looked naive and suffering from a bout of wanderlust. My family has always come first and while I'm proud of that tenet, my choice to leave one place or another could have been softened by better communication on my part. Regardless, one has to follow his/her heart, seek God's will and try to be fair with the organization that's being left behind. And with the one that has just stolen your heart.
Resources for the road from Brazen Careerist
8 On-the-Job Rules You Unfortunatley Won't Learn in College
5 Reasons Why Being a Control Freak is Good For You and Your Career