Are there any studies into the size of the blockchain scaling over time?
Satoshi Nakamoto addressed this issue in the original crypto forum thread.


  Long before the network gets anywhere near as large as that, it would be safe 
  for users to use Simplified Payment Verification (section 8) to check for 
  double spending, which only requires having the chain of block headers, or 
  about 12KB per day.  Only people trying to create new coins would need to run 
  network nodes.  At first, most users would run network nodes, but as the 
  network grows beyond a certain point, it would be left more and more to 
  specialists with server farms of specialized hardware.  A server farm would 
  only need to have one node on the network and the rest of the LAN connects with 
  that one node.
  
  The bandwidth might not be as prohibitive as you think.  A typical transaction 
  would be about 400 bytes (ECC is nicely compact).  Each transaction has to be 
  broadcast twice, so lets say 1KB per transaction.  Visa processed 37 billion 
  transactions in FY2008, or an average of 100 million transactions per day.
  That many transactions would take 100GB of bandwidth, or the size of 12 DVD or 
  2 HD quality movies, or about $18 worth of bandwidth at current prices.
  
  If the network were to get that big, it would take several years, and by then, 
  sending 2 HD movies over the Internet would probably not seem like a big deal.