What's the best way to back up the list of installed apps on your Mac? As I understand, Time Machine or for that matter, any backup solution doesn't backup your apps (for technical reasons, I know).

So what's the best solution to remember/backup the list of apps you have installed on your Mac in case it just stops working one day?

Apart from the obvious "manually write down the name of the app on paper", of course.
Time Machine does back up your applications. You can restore from a Time Machine backup and your computer will have the system software, applications, and user files it had when it was completely backed up. See this Apple page for details.

Some other backup solutions (such as Crashplan) generally are set to just back up the /Users folder - Time Machine is a "bare metal" backup.