Pacman

Finding orphaned dependencies:

pacman -Qdt

Finding explicitly installed packages:

pacman -Qet

Changing status of a package (useful for those things that show up as orphaned dependencies that are actually important, or changing dependencies that were explicitly installed into proper dependencies):

pacman -D --asexplicit <package>
pacman -D --asdeps <package>

Show packages that are not from standard repos. This also shows legacy packages that have been removed from standard repos, and may no longer be required.

pacman -Qm

Checking size of installed packages (requires community/pacgraph):

pacgraph -c

Showing dependency graph (saves SVG file in home dir):

pacgraph -s

Clean old crap from package cache (with dry run to see what would be removed):

paccache -d

Finding the package that contains a particular file (requires extra/pkgfile):

pkgfile --update (updates the meta-data DB)
pkgfile <file>

Rebuilding a package from installed system:

bacman <package>

Finding which packages come from a particular repo (useful for 3rd party repos):

paclist <reponame>