Cryptonite
Cryptonite is not actively maintained any longer
Introduction
Cryptonite brings EncFS and TrueCrypt to Android. You can browse, export and open EncFS-encrypted directories and files on your Dropbox and on your phone. On rooted phones that support FUSE (e.g. CyanogenMod) you can also mount EncFS and TrueCrypt volumes. TrueCrypt is only available as a command-line version at this time.
I haven't had any backdoor requests yet. Watch closely for the removal of the previous sentence.
Get Cryptonite
Cryptonite is no longer available from Google Play. Bleeding-edge alpha versions are sometimes available here. Report bugs to the issue tracker.
More information
What's new? See changelog.
Read up on important security considerations here.
How can I access encrypted Dropbox volumes when I'm offline? Why can't I decrypt and encrypt on the fly? See the FAQ.
Want to build your own apk? See build instructions.
Want to see Cryptonite on F-Droid? Vote here.
Encrypt your Dropbox with EncFS
GNU/Linux
This is simple and straightforward. The default packages should work just fine. There's a nice tutorial on Webupd8.
OS X
MacPorts provides EncFS and works just fine on all OS Xen that I've tested (10.6, 10.7 and 10.8). The MacPorts installation takes some time, but it's definitely worth it. Once installed, simply do:
sudo port install encfs
If you use homebrew:
brew cask install osxfuse
brew install homebrew/fuse/encfs
To make your decrypted folder look a bit prettier, use
encfs -ovolname=Dropbox -ovolicon=${ICONFOLDER}/dropbox.icns ${ENCRYPTEDDIR} ${DECRYPTEDDIR}
Let me know if you need a hi-res icons file.
Windows
encfs4win works fine for me.
Windows & OS X
You can also use the cross-platform frontend encfsmp, if you don't want to use command-line tools.