NOTE: All example commands are used with the package: apache-1.3.6-1.i386.rpm

Installation/uninstallation commands

Install a package
rpm -ivh apache-1.3.6-1.i386.rpm
Reinstall a package
rpm -ivh --replacepkgs apache-1.3.6-1.i386.rpm
Force package installation even when a required package is not installed
rpm -vh --nodeps apache-1.3.6-1.i386.rpm
Upgrade a package
rpm -Uvh apache-1.3.6-1.i386.rpm
Freshen a package
rpm -Fvh apache-1.3.6-1.i386.rpm

The difference between freshen and upgrade is that upgrade (-U) installs the package even if a previous version of the package does not exists; freshen (-F) only performs the upgrade only if a previous version the package was already installed)
Uninstall a package
rpm -e apache

Note that only the name of the package is required, no version number is needed
Force uninstallation, even if the package is required by another installed package
rpm -e --nodeps apache

Query commands

List all installed packages
rpm -qa
Show information about a package
If the package is installed: rpm -qi apache
If the package is not installed: rpm -qpi apache-1.3.6-1.i386.rpm
List all the files that belong to a package
If the package is installed: rpm -ql apache
If the package is not installed: rpm -qpl apache-1.3.6-1.i386.rpm
List the documentation files of a package
If the package is installed: rpm -qd apache
If the package is not installed: rpm -qpd apache-1.3.6-1.i386.rpm
Determine which package a specific file belongs to
rpm -qf /usr/bin/ls

Verification commands

Verify an installed package
rpm -V apache
Verify all installed packages
rpm -Va
Verify the package a specific file belongs to
rpm -Vf /usr/bin/apache
Verify an installed package against a RPM file
rpm -Vp apache-1.3.6-1.i386.rpm
Determine if a RPM file is corrupt
rpm -K apache-1.3.6-1.i386.rpm

If the output of the above command contains the string 'md5 OK', then the package is not corrupt (very useful to check the validity of downloaded package files)