SourceForge, BerliOS Tucows and Softpedia
If an application is very new, or if your distribution's packagers decide that certain applications are not to be included on the repositories, you can still find and download these applications fromwebsites like SourceForge. These downloads come in the form of gzipped or bzipped tar files which contain the source-code. You generally have to extract the source code to a folder, compile the code and install the application. Going into detail is out of the scope of this article, but the most common instructions for installing applications from source code are:
$ make install
This will check your Linux environment, compile the application, and install it.
SourceForge contains almost every type of application imaginable, from open-source accounting applications to videogame emulators and everything in between. You can either browse for software by category, or by its name if you're familiar with it. Once you find the application, it's as simple as download the project's files, extracting them to a folder and typing the above commands to compile and install it. Be warned though, this way of installation doesn't check for dependencies, so if that application depends on certain libraries or software that's missing on your system, you will have problems. Checking the bundled README or INSTALL files in the downloaded archives will point you in the right direction.
Other noteworthy mentions are BerliOS, Tucows and Softpedia. These websites, while not as large as SourceForge, do their part in distributing Linux applications. Just like on SourceForge, the downloads will come in the form of zipped tarballs which have to be extracted, compiled and installed.