There was a time when, if you wanted to be sure a Linux distribution to work on any PC, you almost had to include some proprietary firmware for graphic and Wi-Fi drivers. Those days are long gone. Hardware component manufacturers tend now to either include open Linux drivers or open up their specifications enough that Linux developers can created their own drivers.
Today, the most common reason to include proprietary software is to provide video and audio support. The most popular video and audio codecs, such as Adobe Flash, Microsoft WMV (Windows Media Video) and MP3, are proprietary. While there are open codecs like Ogg Vorbis, they tend not to be used very much.
More rarely, you'll find distributions that include proprietary software to provide additional functionality. The most common is likely Mono, which enables developers to create .NET programs for Linux.
You won't find any of the above codecs in the FSF's (Free Software Foundation) list of preferred distributions. Utoto, a Spanish-language distribution, was the first distribution to win the FSF's favor. GNewSense, which is based on Ubuntu, is perhaps the best known of the free-software purist Linuxes. The two newest members of this club are Trisquel, another Ubuntu-based distribution; and Kongoni, which is designed to get the most from minimal hardware and bandwidth resources. Of them, I'm fondest of gNewsSense.
These distros all work quite well. As FSF operations manager John Sullivan said in a statement, "While others continue to propagate the outdated claim that it's too hard or not possible to make distributions without proprietary binary firmware and other non-free programs, free software activists and developers working on projects like Kongoni and Trisquel continue to prove them wrong."
True, but let's say you want Flash, access to .NET programs and all the rest. In that case, you want another distribution. Most Linux distributions include some access to these programs, but a few embrace proprietary software.
Easily the best known of these programs is openSUSE and its commercial big brother, Novell's SUSE Linux. Their focus is not on multimedia, but on interoperability with Windows. Some people hate hate the SUSE family for its Microsoft connection. I as a pragmatist like them.
Mint, yet another Ubuntu-based distribution, is best known for its integrated media codecs. I also like this distribution.
So which way should you go? If you want to be free of proprietary software, then you'll want one of the FSF's favorites. If you take a more pragmatic view of Linux, you'll want one of the other, more well-known Linux distributions.