I've gone back and forth on whether or not to backup applications. Backing up user preferences for applications is a must, but the value of backing up the actual application files is more up in air.
One of the things that makes this hard to mandate a backup rule about applications is the fact that applications act differently on each platform.
Mac
The Mac might be the one platform where I could see backing up the applications. Most Mac applications are self contained and can be recovered by simply dragging and dropping them back into the Applications directory. The only issue to watch for is an application's size, which could get pricey for remote backups. If that's not a concern I would say, for the Mac, backup your applications.
Windows
Windows applications are different since they install, not just the applications, but a lot of other auxiliary files and registry entries. Running applications without all these other files can have unexpected results. It makes more sense to backup the installer programs and not the installed application.
Remember to also backup the Application Data folder in your user directory. That's where all your preferences are stored for most of your applications.
Linux
Although Linux doesn't have a registry, applications do install a lot of data into various directories in the system. There's /usr, /usr/local, /var and so many others that it's hard to tell if you've gotten everything or if the permissions are right once you've recovered your data.
Luckily with most Linux distributions, all the applications you have installed are in the central repositories and can just be reinstalled with a simple command line call. There's no need to backup most of them when they can all be gotten from a central online location.
I will backup things that I've installed myself, usually under my home directory or in /opt. It's also important to backup application preferences in your home folder. But, you don't need to backup your applications under Linux.
Conclusion
In general, for Mac, go ahead and back them up. For Windows, don't bother, but backup the application installers if you can. For Linux, backup a list of the applications you have installed, then just run your package manager to get them all back out again.
Have any other ideas on how to backup installed applications?