Google probably assumes that you'll check GMail using two different user accounts in Windows, thereby having two different sets of cookies. I'm certainly not saying it's right, though. If I only had one computer in the household, my wife and I would probably use the same login. I hate dealing with multiple user accounts.

But if it were just me checking multiple GMail accounts? Well...I simply wouldn't! I'd just combine the two and only have to check one account. GMail is so good at drawing in many different accounts, and I have at least 10 going into mine at the moment. I use it for work and personal, and just filter with labels. It's great.