How can I get my node listed on Blockchain.info's connected nodes list? We are running bitcoind on our server and its blockchain is synchronized with the network. Do we automatically become a node and get listed on http://blockchain.info/connected-nodes, or is there something we have to do to be seen by the network?
Running BitcoinQT or bitcoind you are a full node in the Bitcoin Network - you receive and transmit Blocks and Transactions. Even better, if you have port 8333 open on your router and machine, other peers can connect to you which is also very useful for the Network.

To be listed as a node connected to blockchain.info, you need to connect to their client (with a specific runtime parameter for example, or by chance). I am not aware as to what IP they are using. However, you don't need to be connected to blockchain.info to be a node - being connected to anyone else on the Network using the standard client makes you a node.