Due to recent demand, I had to figure out how to install the Google PlayStore on Android without all the other apps coming with the GApps package. Here is how to install the stand-alone PlayStore. Hint: Your device has to be rooted in order for it to work.
1. Download the GApps package corresponding to your ROM from http://wiki.rootzwiki.com/Google_Apps.
2. Open it and extract following files from the system/app folder within the zip: GoogleLoginService.apk, GoogleServicesFramework.apk, Phonesky.apk and, if existing, GmsCore.apk.
3. Copy these files to your Android device and move them with any root-capable file browser to: /system/app
4. Change permissions of the files to 644 (same as all the other apks)
5. Reboot
After that, you should see the PlayStore app on the device and it should work just fine. This was tested with a custom CyanogenMod build running Android 4.1.2 on an HTC Incredible S.