Flash is not a part of web. But unfortunately it is mostly used by sharing video services. It is a problem if you running an operating system where the flashplayer plugin is not available (64 bits Linux or Smartphone terminal).

I will introduce 2 ways to read Youtube videos without flashplayer.

Gnash

Gnash is an open-source (GNU) flash movie player. It is mostly available on major Linux distributions. It perfectly works with Youtube. If you want to install it on Ubuntu, you should first remove official flashplugin if any. Then, type:

Same for debian. For Fedora:

In Firefox options, you have to blacklist youtube.com's cookies or it won't work. I tried it, and it works fine with Youtube. You can select video quality, modify the volume, switch to full screen mode and enable/disable notifications on video.

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Greasemonkey script

Greasemonkey is a firefox plugin wich allows you to apply modifications directly into web pages. There is a script named "Youtube without flash auto" wich replaces the flash player with your favorite video player's plugin (VLC, Totem, mplayer...). So, you need ton install Greasemonkey first. Then, install the script. For each Youtube video, it will display a toolbar:

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With this toolbar you can Download the video, or replace the flashplugin with your favorite video player's plugin. It needs less CPU and memory load.

Thanks

This is my first article in english, thanks to Manu for the corrections.