Xplore file browser
It's trivial to replace the independent pieces of xplore, but it has so many features in one app that I just can't let it go. It's got dual pane file browsing, disk usage chart, smb, ftp, and many other cloud storage connections. It also handles many types of compression.
It's become my main offline music player as well, because it has the simple ability to shuffle a folder of music, which is all I really need.
It can also view installed apps, export them to apk, and view and modify appdata (as non root!).