Why do all addresses begin with "1"? Why can't we just delete it? The title is the question :)

All the addresses I have seen - from the very first block http://blockexplorer.com/b/0 to the very last one http://blockexplorer.com/b/229850 all begin with "1".

Why is that? And - if it's really like that - why do we need the redundant number there and not just cut it and make the addresses 1 letter shorter?
If an address begin with "1" then it's a hash of a public key, "3" for a script hash, "5" for a private uncompressed key, etc

You can find a list of all prefixes here: https://en.bitcoin.it/wiki/List_of_address_prefixes