I generally don't advocate full automation of a Twitter feed.  Twitter is great for interaction, conversation, and true connection.  When it's just a bunch of bots broadcasting, it takes away from the experience.

However.

I do think that integrating a feed of new posts from your forums into an interactive Twitter stream can be a good idea.  It just makes sense to take advantage of social tools to promote your online community.  Just ensure that you are active and responsive when someone replies to the Tweet, and you can bring fresh attention to your community.

Both Hoop.la and Eve Community offer RSS feeds that can be pulled into a third-party Twitter manager like magic.

Here's how to do it using Hootsuite. (If you know how to do it with a different Twitter client, please feel free to post in a comment--Hootsuite is my tool of choice.)

1. Grab your RSS feed address.  In Hoop.la, go to the forum you want to use, and see "RSS feed for this forum" in the right column.  For Eve Community, go to the control panel, under Forums, Content Management, click the Content Island tab. Create the Content Island with whatever parameters you desire, then in the Content Island preview window, at the bottom, you’ll see the RSS feed options.
2. Copy the RSS feed address to your clipboard.
3. Open Hootsuite (or your preferred Twitter management tool) and click Settings.
4. Select RSS/Atom.
5. Click the “plus” icon to Add New Feed.
6. Paste the feed URL at the top.
7. Choose your parameters (which Twitter account to use, how often to update, etc.).
8. Where you have the option to add custom text, you might want to put something like “from the forums.”
9. Click Save Feed.

After you’ve done this, new content from your forums (whatever type of content you selected for the content island) will automatically be posted as a Twitter update on the schedule you set up.  Magic!

Keep the magic going by being interactive too, don't just "set it and forget it."  Reach out to your Twitter followers, promote their content as well, and use it to truly build a community that extends beyond the borders of your own platform.

Update 7/9/12 - I had originally posted that Tweetdeck did a similar function, but it appears that was incorrect.  Sorry for any confusion!