Advantage #1 - Stability
If you have used other operating systems, once you have made the switch to Linux, you will notice that Linux has an edge over Windows here. I can remember rebooting Windows many times over the years, because an application crashed, and I couldn't continue working. Linux can crash also, but it is much harder to do. If an application crashes in Linux, it will usually not harm the kernel or other processes.
Advantage #2 - Free Software
Most software can be obtained without cost for Linux. For example, one thing that has kept people from Linux is the lack of office software. That has changed with Open Office, and now you can edit documents and presentations from the popular Microsoft software. The conversion isn't 100% perfect, but it has worked remarkably well in allowing me to correspond and use documents that people send me via e-mail or the web.
Advantage #3 - Runs on old hardware
If you have an old 386 or 486 laying around collecting dust, you can use this to run Linux. I remember running Linux just fine on a Pentium 100 with a 1 GB disk drive, and 16 MB of memory. One use of an old machine like that could be a file server. Just go to your computer store, buy a large hard disk (as long as your old stuff can support it), and you can make a great storage server. With all the digital pictures and movies around today, this could be a great use for Linux. Look into using Samba, a server application for Linux that allows you to make your machine share the disk as a Windows share.
Advantage #4 - Security
Linux has the advantage of the code being in the public domain. This can be a double-edged sword; while you can look at the code, and developers can fix holes rapidly, it also means hackers can find bad code. I have been very impressed with the security of Linux, and the programs that run on it. I think having the code out in the open, and the ability to fix things yourself if necessary is a big plus. Who likes to work blind? With some distributions, on installation the computer will ask you what levels of security you would like for your system. You can be very trusting, or you can be paranoid. Linux gives you this flexiblity.
Disadvantage #1 - Learning curve
I won't lie to you; Linux is going to take some time to learn. I know that our society likes to be instantly gratified. Learning Linux is definitely worth your time, but to really master it, you will need to spend some good time in front of your machine tinkering with things. Don't expect to be an expert after reading something like "Linux for Dummies". If you are contemplating this for your company, you will need to budget some money for training and learning time.
Disadvantage #2 - Equivalent programs
While I gave the example before of an office suite of programs that is working well, there are still applications that do not exist in Linux. Thankfully, this list has become much more narrow in recent months. You will want to think carefully when you switch to Linux about what programs you currently use, and if they have Linux support for them. It may not make sense for you to switch if you are going to spend tons of time converting databases and application data.
Disadvantage #3 - More technical ability needed
You will want to make sure that you train someone in Linux really well. Alternately, you could hire someone who has experience with Linux. A good Linux administrator needs to be on hand as you start to migrate your systems over. This is a disadvantage financially, at least in the beginning. You may find over time, however, that you only need a temporary administrator to handle the routine tasks.
Disadvantage #4 - Not all hardware compatible
Some of the latest and greatest hardware that is being produced is not compatible with Linux. At least, not yet. The people that contribute program code and drivers to the Linux kernel are great at including support fairly quickly. Until that time, not everything you buy for hardware in your system may work. I've had to rely on third-party drivers and other means to make hardware like a new Ethernet card work. Eventually, the support will be built in. One thing you can do is before your purchase, ask if the hardware vendor has support for Linux. Some manufacturers do write their own Linux drivers and distribute them with your purchase, making it very easy to integrate with your existing system.