You are going to get a lot of persona replies to this one, like asking people what's their favorite color (even though everybody know blue is the best), rather than empirical. The general consensus is between two (three if you are rooted, but I'm assuming you aren't if you are asking the question).
Lots of people use and recommend Astro File Manager. It used to be my choice as well, and is very capable.
The other, and my current personal choice, is ES File Explorer. It's full explorer capabilities, even root browsing option if you are an advanced user. Not to mention FTP, cloud integration (Box, dropbox, skydrive, sugarsync, and gdrive) and a decent app manager. All in a nice tight pacakge that's regularly updated. There are a few add-ons as separate downloads if you want them, like a security/antivirus scanner, bookmark manager and task manager. Just a hard package to beat.
Free Tip: You can use ES explorer app manager to make shortcuts, including to apps that have been hidden on the LTE by default. Just go to app manager > category > all... You can long press any of the apps listed to create a shortcut, including one to the 'downloads', PDF Viewer, Polaris Office, Tune In Radio, and Sound Hound, which aren't included in the app tray. Many people download an app that JUST does shortcuts, when this can do that and so much more.
