Probably not, but having the serial number gives you at least some chance of recovery. Without it, even if the police find your laptop in a stash of stolen property, you would have no way of proving it's yours.
And no, booting the computer, entering your password, and showing your files won't work--unless it's recovered in the first few hours after the theft. Stolen computers' hard drives are almost always wiped clean of any record of the lawful owner.
[Have a tech question Ask PCWorld Contributing Editor Lincoln Spector. Send your query to answer@pcworld.com.]
So it's important to keep a written record of your PC's serial number--and make sure that record isn't stored exclusively on your PC. Put it on paper or in the cloud.
If your laptop is stolen, report the crime to the police, and give them the serial number. They're not going to put their top detective on the case, but if they happen to find your PC, they'll contact you.
But you can do some detective work of your own. Check Craigslist for a laptop that sounds like yours. Don't stick to your immediate location; search in nearby counties as well. If you find something that really matches your property, report it to the police.
And yes, I know someone who recovered his stolen bicycle this way.
To greatly increase the recovery odds while you still have your laptop, you can subscribe to a special service such as Absolute LoJack. Your laptop likely already has the hardware built in, but it's useless without the $40-a-year-subscription.
Another service, GadgetTrak, charges only $20 a year.
Both of these services have their own investigators and claim a very high rate of return. But I have no way of testing or judging their claims.
You may get your hardware back, but you will never get the files back from a stolen laptop. What's more, criminals just might get their hands on files that contain your private information.
I've said it before and I'll say it again: Back up your library folders on a daily basis. And encrypt your sensitive files.