Andy Jagoe is zigging while the rest of the mobile world zags. Let everyone else chase the next hot iPhone app. He’s betting the next big thing is a twist on the same old thing: making calls.

He may be right. Jagoe, CEO and co-founder of startup 3jam, is one of several Silicon Valley dreamers who thinks he can reinvent the phone call. And really, let’s admit it’s in need of some Internet-style innovation. We’re in 2009, for crying out loud. Why isn’t call forwarding as easy as e-mail forwarding? Why don’t your voicemails live in a nifty little online inbox?

Remember web 2.0? It’s time for phone 2.0.

And it’s arriving. The most prominent example is Google’s (GOOG) Google Voice, an invitation-only service that offers a free Internet telephone number that forwards calls wherever its owner chooses and delivers features like visual voicemail, call screening and transcription.

Mountain View-based Ditech Networks (DITC) has a similar invitation-only offering called toktok. San Francisco-based 3jam, which is open to the public and starts at $5 per month, adds tricks like convenient group text messaging.

Voice apps are coming

Not everyone is a fan. Apple (AAPL) caused a stir last month when it barred Google Voice software from the iPhone App Store, saying it duplicates features the handset already provides. But Jagoe thinks the services will prevail eventually. “It’s going to be hard,” he says, “to prevent this kind of functionality from appearing on a phone.”

Indeed, people who use these services swear by them, and in Silicon Valley these days it’s a growing cohort. (At a mobile technology panel this month at Microsoft’s (MSFT) Mountain View campus, Google Voice users outnumbered Amazon (AMZN) Kindle users five to one.) The reason is simple: phone 2.0 is liberating phone calls the same way webmail liberated e-mail a decade ago. Now you can keep your phone number, your call history and your voicemails no matter how many times you move, change jobs or switch carriers.

Over a burger at a San Francisco lunch spot, Jagoe explains why this revolution in phone calls is happening now. First, it recently became more affordable for startups like 3jam to forward calls to landlines. Second, Neustar (NSR), a company that enables text messaging, this year gave Internet-based phone numbers a boost by allowing them to send and receive text messages. And third, mobile consumers increasingly crave better options for managing their conversations and staying productive.

Of course, even if the masses are ready for a phone call revolution, there’s no guarantee they’ll buy it from 3jam. If Google Voice opens up its free service to the general public soon, it will get a lot tougher for Jagoe to sell monthly plans. And then there’s the threat from the phone giants: Glenn Lurie, president of Emerging Devices at AT&T (T), tells Fortune that he’s keeping an eye on Internet-based voice services. Clearly carriers would prefer to be the ones selling those kinds of features.

Regardless, Jagoe has a couple of things going for him. 3jam recently finalized a deal with Peek, maker of the eponymous e-mail device, where 3jam will offer phone numbers to Peek users. With those numbers, users soon will be able to more reliably send texts as well as e-mails, and even get voicemail transcripts.

Perhaps more important, Jagoe is running a lean operation, having recently cut 3jam’s full-time payroll from 25 people to 5. He says the company is on track to be cash flow positive by the end of the year, which should help him to avoid the fate of VoIP peers like Yoomba and Jangl that burned through cash before they could figure out a long-term business model.

In the end, the business part has to work. Even in the phone 2.0 world, if you can’t pay the bills, you get disconnected.