Poweramp - best music player for Android, period.
TriangleAway - resets the flash counter that Samsung (and a few other manufacturers) put on their devices. Necessary if you plan to flash custom kernels and ROMs while keeping your warranty.
Astro File Manager - great file browser. Allows for easy moving/manipulation of files and folders. Has Google Drive, Dropbox, and Skydrive integration.
Flipboard - not exclusive to Android, but great for managing multiple news sources.
There are plenty more, but I think those are essential.
[Edited on 12.02.2012 11:38 PM PST]