There are several main 'flavours' of PackageManagementTool in use in various LinuxDistribution. These include:

rpm

Redhat Package Manager. Obviously, RedHat uses this, but Mandrake and a handful of others do as well. File format is RPM.

dpkg

This is Debian's package manager. KnoppixLinux, Progeny and other LinuxDistributions are "Debian-based". File format is Deb.

.tgz

Slackware uses TarBalls that include pre-and post install scripts.

ports

This is the source based PackageManagementTool that BSD uses. Several LinuxDistributions use a similar idea.

portage

GentooLinux?' version of source based PackageManagement, driven by a tool called emerge.

spells

SorcerorLinux? has a 'spell book' approach to source based PackageManagement.

Frontends to these tools include:

up2date

a front-end to rpm provided by RedHat. You get to use it on one machine per user free, and can pay for the right to use it on more machines. It's probably worth it for most users, as it makes installing new software and keeping up with upgrades really easy.

apt

one of the best tools around. It traditionally wraps dpkg, but there is an AptForRpm variant now (and rapidly gaining popularity). It was the first front-end to nicely handle dependencies: apt-get install foo will automatically download and install not only foo, but also any unfulfilled dependencies foo may have.