Twitter is growing at breakneck speed, and major brands can no longer afford to ignore it. According to social media guide Mashable.com, Twitter grew an astounding 752 percent in 2008. And according to market tracker Hitwise, traffic to Twitter went up 43 percent after Oprah joined Twitter on her show. For comparison, Facebook grew about 85.7 percent in 2008.

Two major companies – Dominos and Amazon – recently learned the hard way that they can’t afford to sit on the sidelines and ignore Twitter while customers drive conversations about their brands.

Chances are you’ve heard about the Domino’s Pizza YouTube fiasco, where two (now ex) employees posted a video of themselves preparing food in a very unsanitary way. The blogosphere erupted with angry comments from concerned customers. But rather than proactively addressing the situation, Domino’s kept quiet. Until the discussion moved to Twitter, at which point Domino’s joined the conversation and responded to comments via a Twitter account it established for that purpose. @dpzinfo now has 1,433 followers on Twitter. It also created a YouTube video, which according to AdAge.com has received more than 330,000 views. Richard Levick, president of PR firm Levick Strategic Communications, said he’d give Domino’s “an F for its reaction during the first 24 hours and an A for everything thereafter.”

Another interesting example of how customer conversations are driving company action is Amazon’s reaction to customer complaints. When Amazon recently removed books with gay and lesbian themes from its search results, Twitter users were angry – and very vocal. Amazon quickly broke its silence with statements over Easter weekend to address concerns and offer an explanation via Twitter. @amazondeals has 8,547 Twitter followers.

Jeremiah Owyang, a senior analyst at Forrester Research, recommends that brands secure their own domain names in social media networks and build a community. When a crisis happens, brands can use that community to their advantage.

Some companies have taken heed and embraced Twitter effectively. Instead of waiting for a crisis to begin using Twitter, JetBlue, the discount airline, regularly engages with customers. There have been numerous accounts of @JetBlue responding to passenger inquiries on Twitter by offering advice, directions or assistance in real time.

Actively engaging with customers via Twitter is no small feat, and it is up to each company to decide how much it wants to invest in the network. But for the sake of their brands and reputation, industry giants are realizing one by one that the benefits of embracing Twitter outweigh the costs.

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