(FORTUNE Small Business) – FEW NICHES CRASHED MORE SPECTACULARLY during Web 1.0 than the pet sector. In the space of just nine months in 2000, Pets.com managed to raise a jaw-dropping $82.5 million in an IPO, air a $1.2 million Super Bowl ad starring its sock-puppet mascot, land funding from Amazon.com, build a network of cavernous warehouses ... and go out of business without making a penny in profit. When Pets.com rolled over and died in November 2000, it presaged scores of dot-com disasters to follow and slammed the door on online pet businesses, seemingly for good.

So when San Francisco web designer Ted Rheingold co-founded Dogster.com in January 2004 as a kind of canine version of Friendster, the news drew smirks from the few who bothered to notice. How could Dogster, a pet site cobbled together on weekends and launched on a shoestring budget, expect to succeed where lavishly funded pet sites had flamed out? The consensus on Dogster was unanimous: It would fail.

Since its launch, Dogster has indeed failed, repeatedly, in ways its founders never imagined. But that, it turns out, has been a good thing. Dogster has found a way to turn its mistakes into better features. With virtually no promotion, Dogster (along with sister site Catster.com, launched in August 2004) has become a leading social network for pet lovers, boasting more than 310,000 human members, 355,000 profiles of dogs and cats, and a stable of blue-chip advertisers such as Disney, Holiday Inn, and Target. Dogster has even done something Pets.com never came close to doing: It has turned a modest profit. While site founders decline to give details, they claim that Dogster has been running in the black since July 2005. Last year the company said it earned more than $1.1 million in revenue and nearly doubled its number of users.

TED RHEINGOLD, Dogster.com

FAILURE: No one wanted to buy Dogster's pet accessories. PAYOUT: Ditching retail for an ad model yielded a client: Disney.

A LONG THE WAY, THE SITE HAS become a case study in how to fail well—by launching features quickly, seeing what works, and fixing things on the fly. "When we roll out a new feature, we know we're probably not going to get it right the first time," Rheingold says, perched in the startup's loft office in the Potrero Hill section of San Francisco, so close to the Anchor Steam Brewery that you can smell the hops. Companies like Dogster that constantly examine user data—especially the discouraging stuff—are finding the information increasingly vital online. "Instead of working on a feature for months trying to get it perfect," Rheingold says, "we'll work on something for two weeks and then spend two or three days listening to users and fine-tuning it."

Where old-economy giants once boasted of running "zero defects" operations, today's successful Internet businesses embrace defects as a way to get things right. Some management consultants even advise their clients to "get good" at screwing up. "Failure is the enemy of efficiency, but it's the best way to learn," says Robert E. Gunther, a business consultant for Decision Strategies International in Conshohocken, Pa. Gunther encourages clients to make "deliberate mistakes" to learn faster.

In the case of Dogster, Rheingold and partners John Vars and Steven Reading made their mistakes the old-fashioned way—by blundering into them. Like when they decided to resell ad inventory for other sites. "We were practically hugging each other," Rheingold says. "We had figured it out." But the secondhand-ad strategy was a big, fat flop. The revenue was tiny, and most of the available ads were embarrassingly cheesy. Rheingold retrenched and, after a few false starts, came up with a winning business model: sponsorships and large advertising packages. Forget selling Disney a $13,000 banner ad to promote the release of Lady and the Tramp—Rheingold sold a sponsorship package that embedded the Disney name throughout Dogster's newsletters, contests, and messages sent to new members. Disney was so pleased with the response that it is planning additional Dogster campaigns for its pet-related movies. Now the once-skeptical investment community is taking notice. In September, Dogster, which has 14 full-time employees, closed a $1 million initial financing round from a syndicate of angel investors, including TechCrunch Svengali Michael Arrington.

DOUGLAS MERRILL, Google

FAILURE: Google Answers flopped with people seeking specialized information. PAYOUT: Google shut down Answers and instead offered tools for crafting custom search engines; users built 100,000 in the first four months.

FAILING FAST ISN'T JUST A STRATEGY for startups. One of Silicon Valley's best companies at managing failure also happens to be its hottest: Google. "Fundamentally, everything we do is an experiment," says Douglas Merrill, a Google vice president for engineering. "The thing with experimentation is that you have to get data and then be brutally honest assessing it." When introducing new features, Google has remained true to a "fail fast" strategy: Launch, listen, improve, launch again.

During the brainstorming for the Google Toolbar, for example, the development team tried about five times as many key features as made the final cut, and most were discarded within a week of testing. Several of the features in the final version, including custom buttons and shared bookmarks, were prototyped in less than a week. Even when a feature is a full-blown failure, Google prefers to view it as an experiment that yielded useful information. That's what happened with Google Answers, a four-year effort to build an expert answer service that was shuttered in November. "I don't think Answers was a failure, because we incorporated a lot of what we learned into our new custom search engine," Merrill says. "The failures are the things where you don't learn anything."

MUNJAL SHAH, Like.com

FAILURE: Riya, which searches a computer for similar-looking photos, didn't draw repeat users. PAYOUT: Reborn as Like.com, the technology is faring better with seekers of look-alike clothes.

BUT WHAT IF IT'S NOT just a feature that fails—it's your entire product? That's what happened to Munjal Shah. In August 2004, Shah, a veteran web entrepreneur who co-founded the successful eBay-auction-management service Andale, co-founded a new company called Riya, originally conceived as a photo-recognition engine that would help users search and organize digital images on their desktops. Last March, Riya launched its online service to generally positive reviews. But within a few weeks the user data showed that something was very wrong. "About 94% of the people who used the service said they were satisfied or very satisfied," Shah says. "The problem was, they visited once and never came back." This was failure at its most fundamental level. But Shah kept his cool and looked harder at what the users were telling him. Most visitors weren't using Riya to search and organize their own photos, as Shah had assumed they would. Instead, Riya was being used as a web image search tool.

Just eight months after watching Riya sink like a stone, Shah rolled out a completely revamped site called Like.com, which applies visual search to online shopping. The Like.com engine analyzes photos of items such as handbags, jewelry, shoes, and watches, and then retrieves similar-looking items from the web. The abrupt strategy shift already looks promising. Shah won't disclose sales figures, but he says Like.com has outperformed Riya in traffic and revenue. Most important, users come back. Like.com isn't profitable yet, but Shah says he has several years' worth of funding still in the bank. Jewelry, handbags, and clothing are a $15 billion business online, and Like.com plans to grow into other areas, such as furniture and home and garden accessories.

Shah admits that owning up to failure can be hard for someone building a business. "Changing this means acknowledging that your initial vision wasn't right," he says. "And that can be very difficult." Dogster's Rheingold would certainly agree. A living monument to the wisdom of learning from setbacks, he's managed to build a thriving business atop the ashes of his own mistakes. "What I've learned," he says, "is that you have to give up your ego and just let it go."

Those are inspiring words for sock puppets everywhere.