How to check available package versions in rpm systems?

yum For RHEL/Fedora/Centos/Scientific Linux

Provides the command list to display information about installed and upgradeable (and older) packages.

yum --showduplicates list <package>

zypper For SuSE Linux

Can return a detailed list of available and installed packages or patches.

zypper search -s <package>

Adding --exact-match can help, if there are multiple packages.

As a side-note, here is a comparison of package-management commands.

You can use rpm -qi <package name> to have all information of installed package. You can use below commands as well:

yum info <package name>
yum list <package name>
yum --showduplicates list <package name>

The other answers addresses how to get information about the installed packages on the system. To add to that, it is also possible to query the yum repository about available not yet installed packages in addition with the pkcon search command from PackageKit, e.g.

$ pkcon search name xz
Searching by name             [=========================]         
Starting                      [=========================]         
Querying                      [=========================]         
Available       pxz-4.999.9-2.beta.20100608git.fc15.i686        Parallel LZMA compressor using XZ
Installed       xz-5.0.3-1.fc15.i686                            LZMA compression utilities
Available       xz-compat-libs-5.0.1-2.fc15.i686                Compatibility libraries for decoding LZMA compression
Available       xz-compat-libs-5.0.3-1.fc15.i686                Compatibility libraries for decoding LZMA compression
Installed       xz-debuginfo-5.0.3-1.fc15.i686                  Debug information for package xz
Installed       xz-devel-5.0.3-1.fc15.i686                      Devel libraries & headers for liblzma
Installed       xz-libs-5.0.3-1.fc15.i686                       Libraries for decoding LZMA compression
Installed       xz-lzma-compat-5.0.3-1.fc15.i686                Older LZMA format compatibility binaries
Installed       xzgv-0.9.1-3.fc15.i686                          Picture viewer
$

I assume PackageKit is written generic so that it works with apt repositories as well, although I have only experience from using it on my Fedora systems.