We send 40M - 100M emails from our applications each month. We run 3 outbound relays on top of Postfix. We sign about 95% of our outbound mail with Domain Keys using dkim-filter. We also use SPF records for all of our sending IPs / domains. We monitor our sending IP reputation with via Nagios checks and manual review. Use also have checks setup for the most common black lists. Every email that goes out from our applications has an "opt out" link. (This is really important!)
We used to send all of our mail via one IP address. That meant any given spam report could really hurt our deliverability. Today we send from about 10+ IP addresses, divided amongst the apps. If the reputation of one IP goes down because of a false report, we just decrease the volume on that IP until the reputation goes back up.
For our "company" mail we use Google Apps. For our "marketing" mail use Mailchimp.