How can I split my bitcoin wallet? Let's say I have 10 bitcoins. I won't be using 8 of them any time soon. How can I put the 8 in a separate "offline" wallet not related to the bitcoin client?

This would be a good security measure. If the bitcoin client is ever compromised, only the remaining 2 bitcoins would be at risk.

It seems rather reckless to have all of one's savings in the same wallet.
Go to your Bitcoin data directory
Backup your wallet.dat to a safe location
Move your wallet.dat away from the data directory
Start Bitcoin. It will create new wallet.dat
Get an address from the new wallet, save it in notepad
Encrypt the wallet with some passphrase you will remember for a long time
Turn Bitcoin off
Go back to your Bitcoin data directory
Take the new wallet.dat and store it somewhere safe
Move your old wallet.dat file back into the data directory
Run Bitcoin again.
Send 8 Bitcoins to the address you saved in notepad


Now you have two wallet files - one with 2 bitcoins for your normal use, one with 8 bitcoins for keeping them safe. Just make sure not to lose either of the two wallets, or you'll lose your coins.

Keep your wallet.dats backed up and don't run duplicates at the same time.