This seems like a really basic question, but I'm having trouble searching for answers on it. My understanding is that my bitcoin client (Bitcoin v0.7.1-beta) has basically theoretically downloaded the entire transaction history of every bitcoin transaction that has ever occurred. I can see my own transactions in the Transactions screen. Is there a way to see transaction with wallets that I haven't imported or created on this client? I'm just trying to get a full understanding of bitcoin technology here. Is the reason the client doesn't show transactions from other wallets due to:
User friendliness - it would be overwhelming to have to search through all wallet addresses when most people only care about their own (is there a way to override that?);
Technical limitations - it's impractical to consider every transaction in the huge database when you want to list or look up some particular piece of information;
Design limitations - Not every transaction is actually there with all the information necessary;
Privacy concerns - By making it too easy to view others' transactions people would yell out about privacy more vocally;
It's not terribly useful to look up the balance of somebody else's address, except maybe so they can prove they have a certain amount of funds.
These lookups would be slow, because it needs to work through millions of transactions. Creating the indexes that would allow you to do fast lookups on any bitcoin address would take a sizable amount of disk space.
All of them are there - it's a central part of the bitcoin protocol. What if somebody moves all of their money out of their account within a transaction you don't know about? Therefore, you have to know about all transactions, unless you want to be surprised when their payment "bounces."
Adding to Nick's answer, it's worth clarifying that even though the entire history of transactions are available, there's no information directly stating which collection of addresses belong to a particular wallet. You might get some idea of that by looking at the inputs and outputs of transactions, but there's no "wallet id" (or similar) value in the blockchain.