Lots of people run servers on Linux. Without a doubt, the primary reason is to avoid licensing costs.
Imagine if you will, that you work for a small company and you want to put up an FTP server for your customers to use to download files and so forth. So, you can go out and purchase a copy of Windows Server 2008 R2 for around $700. This is for 1 server license and 1 CAL (client access license).
Microsoft Windows Server 2008 R2 Standard - license - P73-04982 - Windows Network Software - CDW.com
If you intend to run a public FTP server with anonymous access...no additional licenses would be required. If you intend to have usernames/password for users and you intend to use IIS, you would need either CAL's (client access licenses) for these accounts or if you were going to have to purchase the Internet Connector license if you intend to give logons to any customer who needs one. A 5 user CAL pack is about $175. (
Microsoft Windows Server 2008 - license - R18-02503 - Windows Network Software - CDW.com). The unlimited option is around $1999 (if memory serves). If you use a 3rd party commercial FTP app that manages usernames/passwords...CAL's are not required, but the purchase of the FTP server would be.
Now, if you contrast that to a Linux server, you can install CentOS Enterprise Linux 6 for free. Then you can install something like vsftpd, for free. Create all of your user accounts for free, and you total out of pocket license fees will be 0. Of course, this requires that you know something about Linux and can configure and make it work. For somebody with a little Linux experience, you can setup a new FTP server in about 30 minutes. I can do it in less than 10 minutes...and that includes loading the OS.
So, there are tons of servers on the Internet that are running Linux. And it's mostly due to licensing costs. Why pay money to Microsoft to host these types of systems when it can be done for free;
--Web Servers: Apache is the most popular and often runs on Linux
--DNS servers (BIND): across the Internet, BIND is the most used DNS server for ISP's and big corporations.
--Mail servers: Many mail systems run sendmail or postfix as bulk sending systems.
As far as security, Linux is built pretty secure...but can always be setup badly and compromise security. However, I do feel that Windows Server, by it's very nature is often setup and administered by people who don't have much in terms of qualifications. Because it looks like XP, Vista, 7, many can simply click around and can manage to get it setup and working without too much effort. Many will often disable firewalls and turn of security features in an attempt to figure out why it's not working and then simply leave it that way. Contrasted to a Linux admin, Linux can be arcane and many servers don't include a GUI of any kind. Thus, you have to have some knowledge of what you are doing to even get it working. If the average person walks up to a Linux command line and the cursor is just blinking they are going to be lost and get nowhere. If on the other hand, they walk up to a Windows server GUI and start clicking around...they may in fact manage to install an FTP server and get it working. But that doesn't mean that what they did is remotely secure.