Nothing stops you from create hundreds or even millions of bitcoin addresses, which can act as "accounts."

Edit: A bitcoin address is a 160-bit number. That number is associated with a public and private key. The only way you can spend bitcoins stored in an address is if you know the private key of that address.

For more information, this video gives a fairly in depth explanation: http://www.youtube.com/watch?v=Lx9zgZCMqXE

I just wondered to myself how long it would take you to use up all the addresses if you created a trillion per second.

3.6e+17 times the current age of the universe. So, it looks like there are enough addresses for you to really go nuts, if you like. Block chain might get a bit bloated though.

Addresses are not added to the block chain unless they receive Bitcoin. There are no checks in place to ensure the uniqueness of the address, since it's virtually impossible to generate the same address twice, let alone an address with a positive balance.

when you create addresses, you can do them offline. Has nothing to do with the blockchain.

Not only does nothing stop you, it's fairly trivially automatable.

Nothing. For that matter, nothing stops you having a hundred bank accounts, but doing so will certainly increase your chances of an audit.

This is exactly what the standard bitcoin client does - it creates 100 addresses when installed.