How many Bitcoin addresses are there? I was wondering where I could see how many unique addresses currently exist in the blockchain, and especially how many of those have a positive balance. Is that data available somewhere?
You could create an index of all addresses and their balances by going over the whole block chain, f.e. using the RPC API.

I quickly wrote this script in Python. Note that I did not verify it! I only made it to give you an idea on how you can iterate over all transactions. Also, there is probably a more time-efficient way to do it by reading the block chain files yourself.

# setup bitcoind as RPC connection to your bitcoind client using JSON-RPC
block_hash = bitcoind.getblockhash(0)
while True:
    block = bitcoind.getblock(block_hash)
    for txid in block["tx"]:
        # you will need to run bitcoind with -txindex to be able to do this
        tx = bitcoind.gettransaction(txid)
        for det in tx["details"]:
            address = det["address"]
            amount = det["amount"]
            # do something with address and amount
            #  f.e. put them in a dictionary (this will take a lot of RAM)
            #  it is more advised to setup a db on disk
    if block.has_key("nextblockhash"):
        block_hash = block["nextblockhash"]
    else:
        break