The next step up in complexity is multiple users. On a network several users can be using the same computer or even the same program on that computer. This is called time-sharing.

If a computer has multiple CPUs, it can do multiprocessing. Rather than a single CPU giving out turns to various programs, the different CPUs can work simultaneously. Speed increases immensely. Of course cost does, too!

It is possible for a computer to use more than one operating system through the use of virtual machines."Virtual" means it's not really there. But programs written for different operating systems are fooled into thinking their required operating system is present.

Common Operating Systems

Originally the operating system was created by each company that manufactured a processor and motherboard. So each operating system was proprietary, that is, unique to each manufacturer. Problem: changing to a new computer meant your software had to be replaced! Not good marketing. So there was pressure early on to standardize things so that software could be transferred to the new (and of course better!) computer. This required more standardization in operating systems.

The winner in the PC market was MS-DOS, Microsoft's Disk Operating System, and its twin at IBM, PC-DOS, also written by Microsoft. Now it's hard to recall those days when each computer had its own unique operating system. More on DOS Commands

Windows versions (95, 98, Me, NT, 2000, XP, Vista, and 7) are operating systems on their own. The earlier versions of Windows use DOS as the operating system and add a graphical user interface which will do multitasking. But with Windows 95 Microsoft released an operating system that can take advantage of the 32-bit processors.

Windows XP is an upgrade to Windows 2000. It comes in two versions - Home and Professional. The Professional version contains all the features of the Home version plus more business features, like networking and security features.

Microsoft: Which edition of WindowsXP to choose

Windows Vista was released in early 2007. It has higher requirements for memory and processor speed than previous versions of Windows. Vista comes in several different flavors for home and business purposes.

Microsoft: Which version of Windows Vista is right for you

Windows 7 was released in late 2009. There are several versions with differing prices.

Microsoft: Which version of Windows 7 is right for you?

The Apple Macintosh is a multitasking operating system that was the first graphical interface to achieve commercial success. The Mac was an immediate success in the areas of graphics production, and still commands the lion's share of that market. Apple made a major marketing error when they decided to keep their hardware and software under tight control rather than licensing others to produce compatible devices and programs. While the Apple products were of high quality, they were always more expensive than comparable products that were compatible with Microsoft's DOS operating system. Apple's share of the computer market has dropped to an estimated 2.4% worldwide and 3.48% of the US market (MacWorld July 3, 2002). This is an example of how a near lock on a market can be lost in a twinkling. 

The current version is Mac OS X, which is version 10. Since January 2002, all new Mac computers use Mac OS X. Subversions are named Jaguar, Panther, Tiger, Leopard.... Most statistics show that Mac are making a comeback (Feb. 2010 - see chart at bottom of page), but the total usage is still low compared to the total number of Windows systems.
 

IBM's 32-bit operating system, OS/2, was a popular system for businesses with complex computer systems from IBM. It was powerful and had a nice graphical interface. Programs written for DOS and Windows could also run on this system. This system has never really caught on for PCs and is no longer marketed. After Dec. 31, 2006, this operating system will not be supported at all.

UNIX is an operating system developed by Bell Labs to handle complex scientific applications. University networks are likely to use UNIX, as are Internet Service Providers. A lot of people have experience with UNIX from their college work. Many computer old-timers love UNIX and its command line interface. But all those commands are not easy to remember for newcomers. X-Windows is a graphical interface for UNIX that some think is even easier to work with than Windows 98.

Linux is an operating system similar to UNIX that is becoming more and more popular. (And it has the cutest logo!)
It is a open-source program created by Linus Torvalds at the University of Finland, starting in 1991. Open source means that the underlying computer code is freely available to everyone.  Programmers can work directly with the code and add features. They can sell their customized version of Linux, as long as the source code is still open to others. You can find more info at the Linux home site. 

By the way, the word Linux is generally pronounced with a short i and the accent on the first syllable, like LIH-nucks. Here is a link to an audio file of Linus Torvalds pronouncing it in English.

Mobile Devices

Mobile devices such as netbooks, smart phones, Blackberries, and Palm Pilots also have operating systems. Some use proprietary operating system (unique to that device) while other use versions of Windows Linux, or other operating systems that are customized for the mobile device. Lite versions of a number of major applications are available to run on these devices. You can link your device to your regular computer to synchronize documents and data.

The chart of estimated sales of smartphones below is from Wikipedia (Feb. 2010) was created by Lester.
 http://en.wikipedia.org/wiki/Usage_share_of_operating_systems

Changes

Other operating systems exist and new ones may still appear and take over the market position of the popular ones discussed above. Nothing in computers is so sure as change!

Microsoft, for example, has adopted a schedule for phasing out online support and updates for its operating systems.  http://www.microsoft.com/windows/lifecycleconsumer.mspx
For example, under this schedule, July 11, 2006, was the EOL (End of Life) date for Windows 98 Second Edition. There will be no more security updates and no technical support of any kind from Microsoft for products that have passed their EOL date.

Which is most popular?

It depends on who you ask! There is no one who can accurately report the true usage of any operating system. Various companies can report what they sold in a particular period of time and combine that info to see their "market share". Internet sites can report the operating systems of those who come to visit them. Someone might be able to estimate the "installed base" for an operating system, meaning the number of computers currently using that operating system. But no one can really tally the whole world, or even a whole country.

The pie chart below shows statistics on operating systems as of January 2010.
http://en.wikipedia.org/wiki/Usage_share_of_operating_systems  The chart shows the median of values from several sources, all of which use data from web browser visits to web sites. This, of course, omits completely any computer that did not visit those sites. But it's the best we can do.

Usage share of web client operating systems.
Source: Median values from Usage share of operating systems.
     Windows XP (58.64%)
     Windows Vista (23.25%)
     Windows 7 (7.70%)
     Mac OS X (5.12%)
     Linux (1.04%)
     iPhone (0.72%)
     Other (1.32%)