There are a number of answers to this particular concern.
First, there's the community of developers that develop the software, and the wider community of other users. It's something of a cliche, but I've always received better support from a user group mailing list than I've ever received from a commercial vendor. In fact, one of the first questions I ask of any vendor I have to deal with is "How can I send a message to/ask a question of your other customers?"
Second, if you're large enough, you do the support in-house. This is part of my role at $dayjob, where the open source version of Sendmail is used extensively. If it breaks, or we need a feature adding, or a bug fixing, it's down to me (and my team) to do it. We might then talk to the community (and feed our changes back, see the release notes for 8.14.0b4 for example) but internally we're the support group. Recipients of this message are not always comfortable hearing it, but so far I've been successful in hammering away at this point.
Third, you can choose to pay for third party support. There are a number of organisations that do (or did) this. In some cases it's a large part of their reason for being -- for example, much of RedHat's success came from being a vendor that large organisations (who didn't or couldn't take point 2 on board) could sign a support deal with. Then there's companies like CollabNet, who provide (amongst other things) commercial support for Subversion, or Sendmail Inc. who do the same for Sendmail. All of these organisations can (and in many cases have) also build on the open source software and provide their own proprietry benefits, tools, applications, documentation, and so on.
OpenLogic are another organisation providing third party support, training, and consulting, but with something of a twist. They have actively engaged with (some of) the open source community, and formed what they call the "OpenLogic Expert Community". As their site says:
OpenLogic and the OpenLogic Expert Community bridge that gap by providing a single avenue for obtaining expert support on over 200 open source projects. OpenLogic's internal technical support team acts as the frontline of support, answering customer questions and investigating incidents. For more complex issues, OpenLogic turns to the OpenLogic Expert Community. These open source experts work in partnership with OpenLogic to troubleshoot and resolve customer problems. Through the Expert Community, OpenLogic is connecting enterprises users with committed, passionate and expert developers dedicated to the success of open source.
This piqued my interest at the beginning of 2006, and I signed up as a member to help out. I've been a bit busy since then, and haven't had an opportunity to do much, but I was fortunate enough that over the Christmas period some queries came in that were in my areas of expertise.
The result's a deposit in to my Paypal account, and a shiny Xbox 360 on its way to me.
As a bonus, there's a regularly updated, informative (and informed) OpenLogic blog.