In this moment I'm using bitcoin-qt.exe, but it is still synchronizing. Is it possible to be a client without download all blockchain?

I think is not convenient that every person has all the transactions of all time, because this data will be very big in the coming years.
Think that in jan-2012 it tooks 500MB, and today (jan-2013) is about 4.5GB... i.e. it grew 4GB last year (http://blockchain.info/charts/blocks-size). Now think how it will be in the next 5 years, knowing that the transactions rate will increase when it be more popular.
I don't know, just vague ideas that come to my mind.

I read that there are 2^160 possible addresses. https://bitcointalk.org/index.php?topic=24268.0

Suppose that a group (with bad intentions) start to create several addresses using bots, what happens if they exhaust all the possible addresses?