The most obvious advantage is price. Aside from the cost of maybe burning a CD, Linux is free of charge.
Linux is also free to use. There is no 25-digit alphanumeric license code to enter. There is no "Linux Genuine Advantage" to accuse you of being a software pirate. If you want it, you use it. No restrictions
There is new malware for Windows systems seemingly every week. Linux doesn't have that problem. Windows viruses and trojans bounce right off of Linux systems. The term Linux Virus is, almost, a contradiction in terms.
And then there is the available software. Imagine a system where you never had to pay for software. You just chose what software package you wanted, then your system downloads and installs it for you so it's immediately ready to use. No sending your credit card number over the internet, no driving to CompUSA, no buying a retail box filled with more and more ads, no additional license code to punch in, etc.
Linux has ways to run Windows programs (using Wine), but I'm not sure about Macintosh programs. Since Macs are moving to Intel processors, that should be a possibility though.
Granted though, Linux is not for everyone. In my own experience, Linux has never gets the latest games, or the best video editing software. But what Linux does do, it does very well...for free.