The most famous of the alternatives to the status quo is open source software. Now, free software of various kinds had been around for decades before it caught on with mainstream businesses. Because of its long history in academia and government, there was some very mature and useful open source software already available when people started paying attention to it. It was the internet that really made the difference. Suddenly, the advantages that commercial vendors had with their distribution networks, marketing machines, service and support capability, and sales teams evaporated. It suddenly became easy to spread information about free software, distribute binaries and source code, provide documentation and support, and create a collaborative development environment at almost no cost via the internet.
Sure, a lot of the open source software was a bit rough around the edges, and with the popularization of the internet came a proliferation of new open source projects, many of which were immature. But the bar really wasn't all that high. Even some of the most widely used enterprise software was either of dubious quality or was vastly over-qualified for the task at hand. Projects like Linux, Apache, PHP, and MySQL were either close enough in quality to their commercial alternatives to be workable, or the commercial alternatives were overkill for the task anyway. Who needs a $7000 Sun server and a $5000 Oracle license for a regional sales intranet anyway?
Many people still scratch their heads at the phenomenon, wondering why individual programmers and even for-profit companies would be willing to donate their efforts to open source projects. That's the subject of many other interesting articles, but suffice to say, many of the beneficiaries of these tools don't care where the idealism is coming from; they're just reaping the benefit. The availability of open source software has made some niches virtually unprofitable (Unix on x86, webservers, scripting languages), and has provided enough competition in others that companies that were on track to completely dominate their markets have had to fight tooth and nail instead (Microsoft's Server OSes).
Other companies took a different path, but it was another one that was only made possible by the internet. Some people realized early on that with a fast, reliable network at their disposal there was an opportunity to centralize IT infrastructure in radical ways. Whereas only a few years before it was necessary for every branch office to maintain a complex, interconnected network of systems, it was now possible to consolidate them, and in some cases to outsource them altogether.
Probably the poster child for this phenomenon is Salesforce.com. Most companies that maintained sales teams had made the transition from rolodexes and file cabinets to computerized databases and lead-tracking tools, but most of these were either non-interconnected, glorified address books or wildly expensive client-server systems. So Salesforce.com started offering a really good sales force automation system right over the internet for a monthly fee per salesperson. And they've become incredibly successful. Their customers are still spending money on software, in some cases a lot of money, but they know exactly what they're getting for their money. And they don't have to shoulder the risk of a botched implementation, worry about scalability, or hire or train staff to maintain the system. And if they end up dissatisfied, there was no huge up front cost and effort. They can just walk away.
Many companies, new and old alike, have embraced this model of selling access to a centralized system rather than (or in addition to) selling software the old way. Sure, web-based interfaces can be clumsy, and the internet can pose reliability and security problems, but there are a lot of ways to deal with those special challenges, and they look minor compared to the dangers of the old way.
In a way, all internet users have experienced this very same revolution in software, but just haven't noticed. If you were to look at a listing of consumer-oriented software for sale ten years ago you would see titles for mapping, mortgage calculators, dictionaries and encyclopedias, games, business directories, book and periodical archives, tax and financial software, and other titles that have now been largely replaced by online services, many of which are free. Once CD-ROM based dictionaries or maps were largely unnecessary, because it was so much more efficient and economical to use the online ones, the market for them completely dried up.