I've noticed that repositories in CentOS have the .rpm extension.
Are there other extensions?
Is .rpm specific to the operating system? i.e. do other linux operating systems have other extensions?
RPM file is not repository. It is type of package that is used in CentOS (and Red Hat and some other distributions). Repository is place that packages are kept and can be downloaded and installed by package manager in your distribution.
Another package format is DEB. It is used by Debian, Ubuntu and their derivatives.
There are also other formats, but that two are most common.