The warranty is there for you in case the laptop breaks - it's just like insurance. You're betting that the laptop will break and the store is betting that it won't - guess who wins in the long run? But that doesn't help if you're one of the 5% that gets a bad one. But, overall, warranties are money in the pocket for the stores that sell them.
If you can get one of the accidental damage warranties, then you're golden even if you use the laptop as a boat anchor!
Next, the manufacturer's warranties are generally for a year - so hardware problems can be fixed within that period. Interpretation of the "hardware" thing is a bone of contention within the industry. If your hard drive dies, replacement is free - but what about reinstalling the OS, drivers and programs? Where I work, we'll reinstall that for free - but other places may not be as nice as we are!
Now, don't forget that you'll lose the laptop for repairs if it dies. For simple repairs locally it may only be a day or two - but for more complicated repairs that have to be sent out, it'll be 2 or 3 weeks! No warranty will cover that!
If you do opt for a laptop, be sure and make the recovery disks immediately! And put them in a safe place so that they're there if you need them. Also, it's essential to backup everything that you can, you may not get a chance to recover it (and data recovery at a PC shop is expensive).
The most common failure on a laptop (that I've seen) is a hard drive failure. The actual repair (assuming that they have a hard drive in stock) takes about 3 minutes. The diagnosis will take a bit longer (an hour or two if it's just the hard drive being diagnosed) and the reinstallation will take a couple of hours. Shops can't afford to have a tech sit over the computer to reinstall and test everything, so they work on many systems at a time - this increases the time the repair will take for you. Doing some of this will save you time, but will increase the workload on you. Specifically, reinstalling the OS is a piece of cake, but updating the drivers and installing the Windows Updates is a real time consuming PITA. You can pay for them to do it, or you can "spend" your own time doing it. The restore CD's will make it a lot less painful - but there's still the Windows Updates to sit through.
Warranty plans generally come in 2 flavors - Repair or Replacement. To mess things up, some of the Repair plans that are sold actually cover systems that aren't economically feasible to repair. So the plan will give you a replacement rather than fixing your system - but that doesn't cover your hard drive's data - so it's up to you to make sure that you've backed up everything that you need.