Read First
Plex for ARM CPU architectures is compiled with very limited transcoding abilities. Do not expect transcoding to work, you will get the best Plex experience by using DirectPlay or DirectStream features and streaming locally. x264 content should play remotely as long your internet connection can support it and client can play back the media's codecs. If your content has subtitles it will not work for transcoding.
It is now possible to install Plex Media Server on ARMv7 devices like the Raspberry Pi 2, Banana Pi, ODROID and others thanks to uglymagoo, jonathanmcalroy and others using the Synology package. The old thread was getting quite cluttered so this one is to have a clean overview of the guides and fixes. It is important to note that this is not officially supported by Plex so you should not expect perfection.
It used to be necessary to run a chroot but that is no longer necessary. If you are moving from the chroot version see jonathanmcalroy's guide for converting to the native ARMv7 package. These methods will not work on a Raspberry Pi B+ and earlier models as they are ARMv6 devices, you may have luck with the chroot version.
If you are on a debian wheezy or Ubuntu 14.04 use the Raspberry Pi 2 or Banana Pi guide as they have libgc6 2.13. If you are on jessie or have an update libgc6 2.19 use the ODROID guide. If you browse to the /lib/arm-linux-gnueabihf look for the ld-2.1x.so file. ld-2.13 means you have version 2.13 and ld-2.19 means you have version 2.19.
Getting Started
Updated August 15, 2015
Raspberry Pi 2 Guides (includes ready image - Media Server Image with and without Kodi)
jonathanmcalroy's Pi 2 Plex Image
ODROID Guides (includes ready image)
FAQ
Why do I get the Server is not powerful enough to play this video?
PMS currently checks via javascript if a server has the resources to transcode and, rather than issuing a warning that playback may suffer, it blocks the video. Hopefully this will change in a future release. For now you can change the javascript file using the nano guide or the vi guide and make sure you are using your external hard drive for Transcoder temporary storage as outlined in the guides above.
Plex can't see my hard drives..
You must mount your drives properly so they have a path like /mnt/movies, you cannot just use /dev/sda1 as the path.
How do I get best playback results?
Use clients that do the decoding of the video so your ARMv7 device doesn't have to transcode. Plex Home Theater should play back everything. Your results will be different with various Plex apps and codecs your videos use.
My subtitles don't work?
~Some clients can support subtitles natively like Samsung TVs. Other clients do not so ARMv7 device has to do heavy transcoding and therefore is likely to fail. I haven't tested external subtitle videos in Plex Home Theater. This may no longer be an issue when the Plex web client supports subtitles inside HTML5 browsers.
My SD card is filling up, can I move the metadata?
The Plex metadata can take up quite a bit of space. You can get a larger SD card or relocate it to your external hard drive using this guide