Microsoft Office is used by hundreds of millions of people, both at home and at work. Whether it's just Word and/or Excel, sometimes it's the whole suite. In the past five years, Microsoft has seen big competition in the Office space, and while they might not be hurting too badly from it, computer users are benefiting from other entries into the space.
Traditionally, Microsoft Office has always been sold as an installable suite of applications that is purchased once and used until it becomes outdated. The basic suite has usually consisted of Word for document editing and Excel for spreadsheets. Additional programs like Outlook (for email), Powerpoint (presentations), Onenote (note taking), and Access (databases) often made the "Ultimate" Office suite too expensive for most. Even the least expensive version was usually pretty pricey.
In the 2000's, the most popular Microsoft Office alternative was the open-source (and free to use) OpenOffice.org, which was purchased by Sun, later by Oracle. It was a popular replacement for the most popular creative applications like Word, Excel and Powerpoint. Oracle didn't handle the product well, though, and it has since become the current [and excellent] product LibreOffice. I regularly install LibreOffice for many of my clients because it's more than capable of handling the basic needs of most users. It's free, doesn't need a subscription, and isn't tied to the cloud, so it meets many people's needs.
Currently, the biggest competitor to Microsoft Office is Google and their Drive product, which offers word processing, spreadsheets, presentations, and more. It's also a free product as long as you have a free Google account, and all your work is kept on the cloud so you can access it from anywhere. Google's office software isn't nearly as full featured as Microsoft's or even LibreOffice, but it does 99% of what most users need on a daily basis. Whether it fits your needs or not will vary from person to person, but I personally use it for everything.
Lastly, the new alternative for Microsoft Office is...Microsoft Office. Their new product, Office 365, is a subscription service. It starts at $70/year for a single user or $99/year for five users. This can be a steep price for some, considering that it used to cost $150 for the software out-right. That's what makes the $99 subscription so appealing to families.
Office 365 can also be very appealing to small businesses as well, where it can handle email in addition to giving them the most recent version of Office applications. For my clients who use Outlook as their primary email client, I've been migrating them from Google Apps to Office 365 because it handles email much better with that application. If you don't use Outlook, I recommend Google Apps for your business.