Is it possible to view others' transactions in bitcoin client?
Is it possible to view others' transactions


Yes.


  in bitcoin client?


No.


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."
There's already a website called Bitcoin Block Explorer that pretty clearly establishes that transactions are public. Even if there wasn't, you could still build your own.