Android - Where in the file system are applications installed?

Where an app is stored very much depends on several criteria:

• System apps / pre-installed-bloatware-apps are stored in /system/app with privileged apps in /system/priv-app (which are mounted read-only to prevent any changes). You may also find system apps in /custpack/app's subdirectories.
• normal apps in internal memory go to /data/app
• some apps (encrypted on internal storage?) go to /data/app-private
• Apps stored on external memory go to an encrypted container in /mnt/sdcard/.android_secure. As at runtime Android needs them to be decrypted, it will decrypt them and store a decrypted copy on tmpfs (so it's gone on a reboot) in /mnt/asec
  (you cannot simply look into /mnt/sdcard/.android_secure directly from the device; but if you use a card reader and attach the card to your PC, you will see the files there have the extension .asec instead of .apk -- from which you will get the connection to the name /mnt/asec).
• the apps data are stored below /data/data/<package_name> (internal storage) or on external storage, if the developer sticks to the rules, below /mnt/sdcard/Android/data/<package_name>.

They are stored in /data/app/ but unless your phone is rooted all you will see is an empty folder.

On my Android 4.0.4 (ICS) Xperia ray, they are stored in /mnt/asec/XXX-1/pkg.apk. XXX is the Google Play ID of the application.
For example, Firefox is found at /mnt/asec/org.mozilla.firefox-1/pkg.apk and Skype is found at /mnt/asec/com.skype.raider-1/pkg.apk.

Following zuul's comment I took these screenshots from my phone to confirm my answer.

Firefox

Stopwatch & Countdown Timer

And these are my phone's details: