Bogofilter is a Bayesian spam filter. In its normal mode of operation, it takes an email message or other text on standard input, does a statistical check against lists of "good" and "bad" words, and returns a status code indicating whether or not the message is spam. Bogofilter is designed with fast algorithms (including Berkeley DB system), coded directly in C, and tuned for speed, so it can be used for production by sites that process a lot of mail.
Fakeroot runs a command in an environment were it appears to have root privileges for file manipulation, by setting LD_PRELOAD to a library with alternative versions of getuid(), stat(), etc. This is useful for allowing users to create archives (tar, ar, .deb .rpm etc.) with files in them with root permissions/ownership. Without fakeroot one would have to have root privileges to create the constituent files of the archives with the correct permissions and ownership, and then pack them up, or one would have to construct the archives directly, without using the archiver.
posh is a stripped-down version of pdksh with several improvements that aims for compliance with Debian's /bin/sh policy, and few extra features. Currently, Debian's policy is to adhere to POSIX with the exception of supporting 'echo -n', so posh strives toward compliance with SUSv3 (with the exception of 'echo -n').