How do I see the IP address of a bitcoin transaction? How do I see the IP address that someone used to send or receive bitcoins with? Is it stored in the blockchain?
No, IP addresses are not stored in the blockchain.

But Gavin Andreson indeed notes that


  Unless you are very careful in the way you use Bitcoin (and you have
  the technical know-how to use it with other anonymizing technologies
  like Tor or i2p), you should assume that a persistent, motivated
  attacker will be able to associate your IP address with your bitcoin
  transactions.


One way to do this is to simply run bitcoin peer-to-peer clients that connect to a large fraction of the active nodes.  It's not as hard as you might think.  See Dan Kaminsky's Black Hat 2011 talk, starting at slide 21, for more.  (Thanks to kirian for reminding me of the link).  Then see An Analysis of Anonymity in the Bitcoin System 2011-07-22 by Fergal Reid, Martin Harrigan for how to link together the various bitcoin addresses that each user uses.

Some related background is outlined by Craig Reading:
Bitcoin Theft – The Top Ten Threats | Genesys Guru Blog