Is it obligatory to backup
wallet.dat after each outgoing transfer?
I understand it is, but not after each incoming transfer.
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Every 100 transactions, counting both sending and receiving. For receiving, you can treat multiple transactions to the same address as a single transaction.
This ensures that you don't lose any bitcoins if, for example, your hard drive crashes.
keypool in Bitcoin-Qt client adjusts this.
You're never obligated to back up your wallet. It is something you do to protect yourself.
You do not need to backup your wallet to prevent from double spending (you spend BTC, loose your wallet, restore from an old wallet and try to spend the same coin). The protocol will stop that from happening because the transfer exists in the block chain.
However, you do need to back up your wallet to know what you have to spend. Without a current wallet the protocol won't know that you own a BTC and that you can spend it.
It is impossible (without a lot of computing power) to double spend BTC. Without your wallet you won't know what you have to spend. You can loose Bitcoins forever just like you can loose cash forever.