There's no substitute for having solid team dynamics, which is one of our top criteria for hiring. However, once you're stuck with the people you've got, there's still some things that can help.
Common Area
The biggest thing that helps us is a "common area" where most developers congregate. Currently 3 large tables (~4 people with plenty of space), plan to add a couch or two soon. This is easier because we have laptops, so it's not a big deal to move around. We usually work in groups of 2-3 on tasks, and try hard not to silo anyone on something for more than a few days. We change up who works with whom frequently (every several weeks or so), so developers regularly rearrange themselves in the common area to sit near the other people they're working with.
Again, this is also easy for us because everyone gets along very well and likes to work with everyone else. The key is not to force it - it's not like Bob and Sarah are told they will work together on task x whether they like it or not, to ensure everyone gets a rotation with everyone else. Rather, we have a fairly diverse set of tasks and people are assigned to a task based on what they are interested in and what their expertise is. If your developers are wary of working in pairs or some don't get along as well, start slow and make a few obvious matches with the most social of the group, so the rest can see how much better it is.
Lunch & Learn
One person from the group presents a topic (say, LINQ providers) to the rest while lunch is catered (pizza or something simple). This lets the presenter choose a topic they are passionate about/interested in; it helps hone presentation and communication skills, and it lets the rest of the group engage in a single individual. This helps build respect/rapport.
Celebrations
When we hit moderate-to-major milestones, we send out a meeting request to everyone to meet at a bar. Sometimes it's on the company, sometimes not. Some people will attend one and skip another, but after a few most people end up going. There's no social lubricant like alcohol.
There is always an unavoidable stigma of "socializing, not working" in organizations large enough that there are other groups nearby. Most of our sibling groups probably think we just cut up and never get anything done, but the only thing that matters is delivering quality that makes leadership look good. If you can goof off and chat while doing that, leadership will rarely complain.