Why does someone join a forum? Common reasons I see are to ask or answer a question, share an opinion, or share work or a hobby. What do these things have in common? They all engage the ego, and they all come with the mindset of "this is serious business." They can easily devolve into rude competition. You can gather a lot of expertise on a forum with this sort of exchange, but you will not have a community.
Setting the tone of your community is an immense challenge, because it requires vigilance and concerted effort. Not only must you set the example through heavy participation, but you must also find and rebuke comments that set a contrary tone. This is a slow process, and sometimes you need to shatter the "serious business" attitude when it gets uncontrollable. That's when it's time to call in the big guns: silliness.
Silliness solves multiple problems at once. First, it just ruins that facade of seriousness. Being silly requires letting go of all that for just a minute. Second, it makes you more real and shows another aspect of you to the other members. Once you've been completely not-serious with someone on the Internet, I find that makes it click in your head "This is a real person just like me," which immediately and permanently changes the context in which you address them.
So what's "silly"? It can be talking about anything other than the main topic of your forum ("So who else here likes taking weekend camping trips as much as me?"). But to really see the full benefit, delve deeper into goofing around, making jokes, and being completely and innocently tongue-in-cheek and off-the-wall. I like to break the ice by playing pranks on members. How did that member's title become "Minister of Mischief"? Who changed all of the moderators' avatars into pictures of Hollywood actors? Be the instigator.
Is this appropriate on every forum? Maybe not. But don't be quick to say "that would never work on my site." I find too many forum owners themselves fall into the "serious" trap and think it would damage their site's reputation to have off-topic banter muddy their site. The irony is that this sort of banter is the surest sign of a truly healthy community that is forming bonds much deeper than the topics at hand.