So, our core backend system is a SQL database with two ASP.NET MVC (C#) web site front ends
1) cheezburger.com, the one that our users use to make content via our tools (Caption tools, graph builder, etc.). It's also a niche social network, where people curate their favorites, message with friends, etc.
2) The internal site that our moderators use to sift through submissions.
Nothing shows up on any of our voting pages without having been screened by a moderator. Nothing shows up on any of our sites' front pages without having been voted on by the community. A lot of what makes things work is the mix of editorial guidance and community feedback. It's not a pure democracy, but it's not a pure dictatorship, either. It turns out that a lot of deliberate thought and hard work goes into running a funny web site. I'm constantly amazed at how our editorial team is perpetually refining their process and sharing knowledge.
The software does things like automatically filter out duplicates and allow moderators to filter by items that have been added as a favorite by members of our community, etc. We also try to automate as many mind-numbing brute force things as possible, to let our humans do what only humans can do (answer "is this funny?") so the submission engine does things like automatically resizes and watermarks images. I personally spend about as much time working on software for around 16 moderators than I do working on software for around 16 million end users. Most of the moderators are in the office with me, and I really love having the low communication overhead of just being able to walk over there and ask "what exactly do you want, again?"
Almost all of our front-end sites are running a single custom Wordpress theme (PHP) hosted by Wordpress VIP (even with the recent downtimes, nobody is better at hosting Wordpress than Wordpress/Automattic). We send content there through the WP XML-RPC API. We use some extra metadata to identify posts as "voting" or "front page", and our theme is able to filter by that. We've also written some custom wordpress code to do things like display the "you may also like", integrate with your cheezburger.com account to add favorites, etc.
Both the content backend and the wordpress frontend are generalized enough so that we can usually get a new site from concept to launch in around a week. Some sites (senorgif.com, for example) require backend changes (support for Animated GIFs).
From a process side, we try to be cutting edge without falling into trendy bullshit buzzwords. We use a variation of Kanban, where we visualize and limit work-in-progress to keep things flowing through our system quickly in a way that allows us to respond quickly to new ideas or emergent problems. Our team is distributed, we use Campfire for multiple rolling discussions. Tokbox for video chat, Skype for screen sharing, and Kiln for distributed source control and code reviews.
With a few exceptions (only one guy really knows Flash) every one on the team is a multi-technology generalist, working on the full stack, top-to-bottom, front-to-back. We generally work in thin vertical stripes rather than thick horizontal layers. As a result, I'm able to have an idea for a feature on Monday morning and have it coded, reviewed, tested, and deployed by Tuesday morning.
We have multiple layers of test automation and monitoring, which allow us to turn around those small releases very quickly with very little manual human testing. We have a goal to do IMVU-style continuous deployment, where every submit to our central code repository would, if all tests pass, automatically trigger a zero-downtime production code update, but we're not quite there yet.