First, we will look at the most popular possible combinations for a dual-boot PC. There are three popular alternatives for an average user. We won't consider Mac systems as they're not used by an average internet user. So the possible combinations are Linux/Linux (e.g. Red Hat & Ubuntu), Windows/Windows (e.g. Windows XP & Windows 7) and Windows/Linux (e.g. Windows 7 & Ubuntu). A Windows/Linux dual-boot system is most popular among users across the world. So let's see some of the advantages of having a dual-boot system.

You get familiar with two different operating systems - This is one of the biggest advantages of dual-boot systems. The more you know about two different operating systems, the more you're well-equipped to work in different conditions. If you're a freelancer or a frequent traveler, at times you may have to work on a computer system having a different operating system other than installed on your own system. Generally, Windows or Linux is the popular choice for users and if you're familiar with both of them through your dual-boot system, you can adjust well in alien conditions while working on a different PC.
You get more choices for applications - This is quite obvious when you're using two different operating systems. Fortunately, both Linux and Windows have big collection of applications for almost every situation. You not only get different applications to complete a task in more than way, but you can also select the best application on either platform that completes the task most reliably and efficiently. It's also a life saver when the same type of application is not working properly on one of the operating systems. In such conditions, you can easily switch to other operating system to get the same application running smooth and fine.
You're more prepared to deal with an emergency (OS corruption/infection) - If you're technically challenged and your operating system gets corrupted or infected, you may lose your precious data. This can also become a nightmare as you have to spend a considerable amount of your time in re-installing the operating system. This also includes the time spent in installing all the previously installed applications and drivers. But, if you have a dual boot system, you can continue to work on the second OS while you repair or disinfect the first one. This not only keeps your productivity intact but also gives you enough time to rectify the fault at your convenience.
You're less susceptible to occasional platform-specific virus attacks - Nowadays almost every PC is connected to the internet which is a boon for all of us. But this internet connectivity can be a curse too. Sometimes a vulnerability in a particular operating system is exploited through mass scale worm or virus attack through the internet. In such circumstances, a dual-boot PC can be a lifesaver. During the time this mass attack is at its peak, you can keep working on other operating system keeping your PC immune from the infection spreading through the internet for that particular operating system.