What is the best operating system and why?

Note: Both Mac OS X and Windows have come out with newer versions as of the writing of this answer. Some details may be different from what is written below, and the answer should be updated accordingly

The best desktop operating system to use depends on what its intended use will be and who will be using it. There is no specific operating system which can be called "the best" overall, and since most current operating systems share most common and advanced features there is much debate on the topic. A few of the most popular operating system, their pros and cons, and some of their best uses are described below. 

Microsoft Windows

Pros:

• The largest library of programs and applications.
• Some commercial games work only with Windows and DirectX.
• Almost all hardware has drivers which are compatible with Windows. 
• Most widely used. 

Cons:

• Prone to viruses, spyware, and adware if proper steps not taken such as installation of internet security software, which reduces performance speed.
• Requires regular maintenance to avoid system errors and reduced performance.
• Even with maintenance, issues can slowly accumulate requiring a re-installation of Windows to restore performance and fix software issues.
• Purchasing a Windows license/install disk can be relatively expensive
• Windows Vista, the most recent version of Windows, has high system requirements.

Notes: 

• Windows Vista has relatively high system requirements compared to its Windows XP and other operating systems. This has caused many individuals and businesses to continue using the older Windows XP. 
• The two most common versions of Windows are Windows XP and Windows Vista. Vista, although it has some issues, does have some new features such as search-as-you-type search and a 3D-accelerated desktop, features up until now only found in Mac OS X and some versions of Linux.
• With the introduction of Virtual-machine software, Windows has become a popular add-on for Mac and Linux in order allow those computers to support Windows-only software or hardware when needed.
• The Windows market share has seen some decrease in recent years and months.

Best uses:

• Gamers
• People who must use Windows-only software for work or school.
• People or businesses looking for an inexpensive computer yet do not have the ability to use Linux.

  

Mac OS X

Pros:

• Relatively simple and intuitive interface with many advanced features. 
• Not a target for virus or malware attacks, generally: there are no Mac OS X viruses in the wild, and with its UNIX base, it is fairly resilient. There are a small number of trojans (malicious software) which have been known to take effect through applications running in Mac OS X, though they are almost always found on illegal-content-based websites and are not of significant concern. Apple has begun integrating malware blacklists into Mac OS X to prevent infection. 
• Second-largest selection of software, with many high-quality Mac-only programs in existence, such as those found in iLife. Although at one point software for certain tasks were not Mac-compatible, most software is now either Mac-compatible or has an equivalent that is. Most advanced games have also recently became compatible with Mac OS X.
• Reliable and high performance. 

Cons:

• Limited to Apple-manufactured hardware.
• Some hardware does not have Mac-compatible drivers, though the number of this hardware has recently become small and negligible.
• In some cases, it may be difficult to do cross-platform network hardware sharing for a Mac OS X based computer in a Windows network or visa-versa. For example, a printer's Mac driver may not support cross-platform printing to a Windows-connected printer, and replacement drivers may or may not exist.
• Smaller library of applications in comparison to Windows. 

Notes: 

• Macs occupy the medium-range to high-end computer market and as such are not sold for the same prices of some low-end PC brands (e.g. the low-end Mac Mini costs $600 USD yet many mainstream low-end PC brand desktops can be purchased for around $400-500). As a result, Macs are popularly considered to be more expensive than PCs, however Macs have been shown to have competitive pricing to comparable PCs (e.g. the Lenovo Thinpad X300 costs about $2,500 while the MacBook Air runs between $1,800 and $2,700 and outperforms the Thinkpad, or the Dell XPS One prices at about $150 higher than a comparable iMac. Additionally, the following factors can cause the total price of owning a Mac to be even less compared than that of a PC: Apple iWork is relatively inexpensive compared to Microsoft Office, PCs experience hardware or software failures more frequently than Macs, increasing service and replacement costs, Macs do not require the frequently expensive internet security software subscriptions.
• Though Mac OS X suffers from relatively very few real-world hacks, security holes in Mac OS X do exist, just like in any other operating system. Also like in other operating systems, they are fixed with software updates upon their discovery. 
• With a relatively low market share compared to Windows, there are still individual programs which are only Windows compatible. However, virtual machine software with a Windows installation or compatibility layer software can allow those programs to run even on a Mac.
• The Mac has seen significant market share increases in recent years and months, something which has also increased the amount of Mac-compatible software. 

Best uses: 

• Students who are not required to use Windows-specific software (though Windows can easily be installed to use Windows software). A recent study indicated that the number of American students intending to purchase Macs has neared that of Windows-based PCs. 
• Home users looking for an easy and reliable computing experience who are willing to pay more than low-end PC prices.
• Graphic designers and photographers.
• Scientists. 

Linux and other UNIX-based

Pros:

• Low number of viruses and other malware, similar to Mac OS X 
• Usually free
• Large selection of Linux distributions to choose from. 
• Has a large amount of free and open source software equivalents to commercial Windows and Mac software
• More easily customizable
• Can run many Windows programs with the use of a compatibility layer such as Wine. (Programs such as Cedega can be used to run many Windows games) 
• Reliable with good performance and low requirements. 

Cons:

• Advanced use and installation of some software may require more advanced knowledge than is required for use of Windows and Mac.
• Many commercial programs do not support Linux
• Small commercial game library

Notes: 

• There are a few main types of Linux: Debian, Fedora, Red Hat, and SUSE. Ubuntu, a type of Debian, is highly popular among home users, as is SUSE, to a lesser extent. Fedora is more popular among businesses.
• There are many other (non-Linux) UNIX-based operating systems (with the same UNIX base as Linux), including Mac OS X and SunOS (which are based on Free-BSD). There are also some UNIX-like operating systems. 
• Through customization and software like Beryl, Linux can be made to have advanced desktop effects similar to Aero on Windows Vista or Aqua on Mac OS X.
• "Dependency hell" can make installation of certain programs on Linux difficult even for advanced users.

Best uses: 

• Experienced computer users looking for a good, free operating system.
• Businesses looking for reliable and affordable computing, so long as they do not need Windows-only software and have a competent IT manager.

Bottom line

Though there is no one clear best operating system, each does have its advantages and disadvantages, and different people will be best using different ones. Microsoft Windows is the most common operating system and is a reasonable choice for most people. Mac OS X is second-most popular (and gaining market share) and is an excellent operating system for those who can purchase a Mac. Linux is a very good advanced operating system available for free and is recommended for experienced users. 

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Mobile Operating Systems

Aside from the main question of which OS to use in your home or work computer, lightweight mobileoperating systems are also used (and almost always pre-installed or even hard-wired) in mobile devices such as cell phones, smartphones, PDAs, and Internet Notebooks/Superportables (which are similar to downsized laptops with low specifications). There is not a great deal of choice among these, and features differences are based more on the mobile device itself, and less on the operating system. Windows Mobile is usually used in Pocket PCs and Smartphones; iPhone OS (based on Mac OS X) is used in the Apple iPhone and iPod Touch; Symbian is used in Nokia, Sony-Ericsson, and other cell phones; and Linux-based mobile OSes are common both on cell phones and small Internet Notebooks.