Linux package formats are the different file formats used to package software for various Linux distributions. These are the principal kinds of package: binary and source packages.
apk — used on Android.
deb — Debian package, originally from Debian. Used by Debian and derivatives such as Ubuntu.
ebuild — the file containing information on how to retrieve, compile, and install a package in Gentoo's Portage system using the command emerge. Typically these are source-primary installs, though binary packages can be installed in this fashion as well. Gentoo-based distributions also use the ebuild system from the same Portage tree.
RPM — RPM Package Manager, originally from Red Hat, is now used by many other distributions as well, like openSUSE, Mandriva and Alt Linux.
pkg.tar.xz — used by Arch Linux's Pacman package manager
PISI is used by Pardus.
tgz or tar.gz — standard tar + gzip, possibly with some extra control files — used by Slackware and others, or sometimes when distributing very simple handmade packages.
SuperDeb — an installer containing a program plus all the dependencies needed, used in Super OS.
LZM — Used by Slax. Opens with Slax Module Manager, and then gets installed to the KDE menu as a Desktop Config file. May be placed into the Slax CD's Modules folder to get installed at boot.
PUP and PET - used by Puppy Linux and derivatives - click and install package type. OS can be installed to a flash drive for portability and will bring apps with it.