It's pretty much impossible, since you can place applications just about anywhere you like. Additionally, what constitutes an "application" might be debatable — does a two-line shell script count?
Regular applications are usually located in
~/Applications (for every user).
Widgets are in
~/Library/Widgets (every user) or
Preference Panes are in
/Library/PreferencePanes(all users) or
~/Library/PreferencePanes (every user)
These are basically the things you'd install manually.
If you installed something using a regular installer, this has been logged to
/Library/Receipts(installer Receipts and the
InstallHistory.plist log file).
If you're using Homebrew, Fink, or MacPorts Unix package managers, they keep track of what they installed. Look up their documentation.
If you installed something manually (QuickLook plugins come to mind), or compiled something yourself, then you're basically out of luck.