Granted, Blogger used its own accounts system until 2006 and only started migrating users in 2007. Four years later it's still not done, but it's close, Blogger will be dropping support for the old accounts soon.
Not only will the accounts stop working, but the blogs associated with them will be deleted if you don't move over to the new system by June 25.
"For a number of technical and operational reasons, we’ve decided to finally end our support for all legacy accounts and blogs after June 25th, 2011," Blogger announced.
"So if you have a Blogger account and haven’t logged in since 2007, you will lose access to the account and associated content permanently unless you update to the Google Account system before June 25th," it added.
Of course, there aren't going to be that many people that haven't logged in since 2007 and will suddenly feel the urge to. But if still care about your abandoned blog and don't want to see it gone forever, perhaps spending a couple of minutes upgrading your account isn't too much to ask.
Google Accounts provides a very solid system, both in terms of security and performance, the two-step verification process is just one example, not to mention it makes life much easier for Google to have just one system for all of its products. You can find out more about the process here.
Google is facing the same problem on YouTube and has issued a similar warning recently, asking users that haven't done so to link their YouTube accounts with a Google one.