In my current venture, we're not yet to the point where we have very many support questions, we're mostly still in "Friends and Family" testing. However, prior to this venture I worked on some other projects, specifically in gaming / gaming server management and for some small hosting companies. With them, responding to support "tickets" if you will was one of our top priorities. However, rather than using an e-mail support system we relied mostly on forums and, for the game, in-game support message systems.

Every company is different and for most of these we were just a bunch of hackers running free communities (with the exception of the web host provider - which was free with premium memberships). However, the importance of answering support quickly was still the same. In terms of the free service, when things didn't work right or we wern't able to instantly respond we were able to write it off as "we're not paid to be here." That didn't always stick though. You might also consider making sure people know what times you guys are generally available. Letting people know that you're not available from midnight to 6am in your local time is a good thing for your users to know.

Depending on what it is you're offering, looking at a message board / forum as a means of technical support might not be such a bad idea. It allows not only you and your team to answer questions (and quickly from almost anywhere you have net access) but it also gives your other users ways to contribute as well. Most importantly, it's an active way to build a knowledgebase, if done correctly. It also saves you from having to necessarily answer the same e-mail's over and over. Even with an e-mail contact available, you could easily put in an auto-responder that lets them know you got it and gives them a link to your support forum for them to browse for a solution in the mean time.

Note: If you use forums, make sure you find some method of making your support posts easy to manage and your official team members easy to spot.