It could be among the most obvious business plans ever: offer to store people’s files online so they can access them anywhere.

The failure of any mainstream computing company to meet that simple need has left a gap now being ably filled by one of Silicon Valley’s fastest-growing startups, Dropbox, a three-year old company reportedly valued at close to $4 billion.

Free software from the San Francisco–based company supplies a “magic folder” into which users can place photos, spreadsheets, and other documents. Stored centrally in Dropbox servers, those files are then automatically synchronized across all of a person’s computers and mobile devices. Folders can be shared between Dropbox users, so when one person adds a file, it instantly appears in another person’s folder. The software eliminates the need to e-mail files between computers or carry data on portable thumb drives.

“Storing and sharing stuff easily is one of those things that was going to be fixed any day now for the last 20 years,” says Drew Houston, 28, who co-founded Dropbox with Arash Ferdowsi, who is 26.

The company, which claims 25 million users, this year reportedly raised $200 million in new funding from investors. Houston says the money will help achieve his goal of turning Dropbox into a universal “data store” connected to the growing array of mobile computers, TVs, and mobile apps that people use. “We’re actually solving a very big problem: we’re building the Internet file system that everything will plug into,” says Houston.

Allowing people to host and share files in the cloud is more complex than it may appear. It is, says Houston, “a serious science project,” whose challenges include the complex “air traffic control” needed to synchronize the more than 12 million files that users upload or update every hour. The company’s engineers had to build software to move all those files around quickly, and needed to design Dropbox’s software to cope with the idiosyncrasies of different devices, from PCs running Windows to iPhones.

Now Dropbox hopes that its software, and its logo of an open box, will become ubiquitous. In June, Sony Ericsson began bundling Dropbox with some of its Android smart phones. Houston says there will be more such partnerships to follow. “In the future, everything will be with you on every device, and the little blue box will be everywhere, whether it’s your phone or your camera, so you always have your stuff,” he says.

Cloud computing is becoming popular among large companies, too, as a mobile workforce demands access to applications from any device. Many companies are using data-storage software from another startup, Box.net, which claims more than 7 million users, and 70 percent of the Fortune 500, as customers. “To store and collaborate, most organizations today have to buy data storage, buy a search product, buy servers, and operate Microsoft Sharepoint [a collaboration tool] and Office on top,” says company co-founder Aaron Levie. Box.net combines those applications, says Levie.

(Yesterday, Box.net said it raised $81 million in funding, bringing the total investors have put into the company in 2011 to $129 million.)

Levie’s latest offering is the Box Platform, which enables software developers to build Box.net into other software. As with Dropbox, the goal is to create a common cloud data store that many programs can access. Both Google Docs and Salesforce.com can already work with the Box.net platform. “Being a platform is the killer app, because we can become the operating system for every business,” says Levie.

Box.net and Dropbox face threats from large competitors now moving into cloud-based storage. Dropbox has been haunted by rumors that Google is set to launch a similar storage service called Google Drive, and Microsoft is increasingly emphasizing office software with sharing features that competes with Box.net. Levie and Houston believe they hold an advantage: neither company has legacy software to defend. “Even if Google launched Google Drive, it is unlikely to work as well with Apple and other products that compete with them,” says Houston. “There’s a lot of value to being independent and focused on one thing.”