How does one attain 1,000+ connections like blockchain.info?
Bitcoin by default will not make more than 8 outgoing connections, and -maxconnections only controls how many incoming connections you allow. Feel free to set this higher, but it will take time before others connect to you in large numbers.

Please don't change this, as there is no need. Connectable peers on the network are a scarce resource, and essential to the decentralization. If people go try connect to all of them like some sites do, we'll very quickly run out.

In case you're a merchant or miner, you perhaps want to set up a few fixed connections to trusted others (see the -addnode command line/config option), but having more connections does not mean stronger verification (the reference client always verifies everything) or even faster relaying (as you'll slow down by distributing new blocks and transactions to all your peers). It is mostly a matter of providing a service to the network.