Zarchiver

There's a bunch of more well known file managers for android, but this one is a hidden gem, if you look for stable operation, and basic archiver functionality without unnecessary bloat, or shady system permissions. It has very clean and simple interface, (not tabbed or dual pane yet), and is capable unpacking multiple-part archives, creating new ones in ZIP, 7z, and TAR formats, supports password-locking, switching current operations to background mode, etc.
File managing is very convenient, especially cutting and pasting files, which works very intuitive. ZArchiver computes md5 checksum, thus letting you check data integrity, supports root access, if device is rooted, and displays hidden files. Main downside of this app is lack of support for online operations, such as FTP protocol, but for that there's another good (open source!) application, Ghost Commander. Also, ZA still remains very lightweight piece of software, and will run very fast even on very slow android devices, unlike some other managers.