I know plenty of people who are diligent about backups. Of course, I also know plenty of people who are not. I also know that every single one of the latter knows they should be backing their data up, and they still don't do it. How do you solve a problem like that?
An immutable, encrypted wallet that can be posted everywhere.
An option for either maximum anonymity (new key each time), or maximum ease of use (a single address), with the latter being the default.
Nags and prompts in the client to make people back up their wallets once they contain over a certain balance.
Store the wallet in my documents, not in %appdata%, so it's actually visible and can be backed up by normal users who do make occasional backups.
Detect DropBox, Skydrive, UbuntuOne and so on, offer to store the file in these online locations by default.
Option to print private keys or deterministic wallet seed to paper as a QR code, and the option to import it again.
Shift attitudes from "works for me, lusers" to "our users are a fragile and delicate resource that must be protected at all costs"