When you first start the new iMac, you will get Setup Assistant, which is more reliable than Migration Assistant based on what others have experienced. If everything transfers okay, hopefully the applications should work fine.
The major problem with Apps from OS 10.6 is that many of them will simply not run on the newest OS. This is not a problem with serial numbers, it's a basic incompatibility.
Adobe and Microsoft products generally require reactivation when moved, this is done with the serial number and/or the activation code. I would have your numbers ready if I were you.
Eustace also brought up a good point, your copy of Quicken will most likely not work, I would check all of your programs, finding out the hard way is not good.