Bitcoin wallet on two Computers

Copying the same wallet.dat to two different computers will initially seem to work, but if you continue to use bitcoin-qt to send bitcoin, the two copies will get out of sync.

The reason for this is the automatic use of "change" addresses. Each time you send an amount less than you originally received, there is "change" that must be returned to you. The developers of bitcoin-qt considered this to be a privacy weakness, as it would make it easier to tell for sure how much was paid and to whom. To make it more private, they generate a new random "change" address in your wallet and send back your change to that new address. To a third party looking at the block chain, it is hard to tell who holds the change address or who was the actual recipient of the transaction.

The reality is that the use of change addresses does little to improve privacy, but sets up new users for a "big surprise" the first time they send a small amount and see their wallet balance temporarily go to zero prior to confirmation of the change. It also makes it unsafe to copy the same wallet to multiple computers.

There are other wallets that give the user control over use of change addresses and that also make the change addresses visible and therefore more understandable.

Another area where other wallets can help is in the generation of new addresses. The original bitcoin-qt wallet generates new addresses randomly. It tries to keep a pool of pre-generated addresses, so that if you copy a wallet it will seem to generate the same new addresses as the original, but eventually the pool of keys will be used up and after that the two copies of the wallet will start to have different contents. The Electrum guys solved this by making the whole wallet "deterministic". That means that all future keys are determined completely by the "seed" and are not truly random. Because of this, you can restore the same wallet on multiple machines and all copies will forever remain in sync.

There are plans to add this sort of functionality to the main bitcoin-qt wallet, but until that is done, alternate wallets are needed if you want to share between computers. Electrum is not the only wallet that provides all these features, but it is the one I am most familiar with. See electrum.org.