Just like commercial software, open source and free software has its pluses and minuses - for anyone who is new to the concept, it's important to be aware of all of these. A small list follows here.
The Cost: In terms of dollars, open source couldn't be better. You pay nothing (unless you choose to donate to the projects), and get a piece of software that you're free to use and install on as many computers as you wish. No annoying anti-piracy dialogs, no serial numbers, or anything. In most cases, you can give copies of the software to your friends without any restrictions.
Timeliness: This is where open source and free software often shines. New versions of the Linux operating system version Ubuntu are released every six months - compare this to two and a half years for new versions of Mac OS X or five years for Windows. For the statistical analysis system R, there might be four months between releases--and smaller updates and new extensions are added constantly. For many open source, programs, bug fixes and new features are added nearly continually. That is, if you're lucky. Some projects lose steam or just plain die--just as happens with some commercial projects. It's worth it to do a little investigation on an open source or free software project in order to see update histories and if there is a prospect for long-term continuation of the software.
User support: This is a little more variable. Some open source programs--such as R--have have excellent documentation, in the form of lengthy user's manuals and active support forums. Others have no formal user's manual and little or no user community. It completely depends on the software package--again, you'll probably want to do a little research.
Compatibility: Here is another area where you'll want to do some homework. For most purposes, many open source programs will read documents from their closed source cousins relatively easily. For instance, OpenOffice.org can open most Microsoft Office documents--unless the latter has some really fancy formatting or odd macros. Export is also usually a pretty reliable thing--and let me emphasize usually. But don't forget--many of these issues plague commercial software, too!
Required Geekiness: Some Linux distributions (basically, "flavors" of the operating system) practically require a degree in computer science to install and use them. Others, such as Ubuntu, are now at the point where a reasonably computer illiterate person could use them with ease. Similar concerns apply to other programs. If you can use Microsoft Office, you can use OpenOffice.org. But, it takes a decent bit of patience to get R working with your data (although it is worthwhile to note that graphical interfaces for R are now out there).