Monkey Raptor

Update Oct 24, 2014

The method with pink background below won't do anything. YouTube (Google Video) has updated (enhanced) their system, back and front.
Nherefour, just use the latest Firefox or Chrome, or update each of them.

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Additional update for February 16, 2015

• YouTube provides HTML5 version of the video player. You can go to www.youtube.com/html5 to find out about your Firefox (or other browser you're using) compatibility, and request the HTML5 player if available.
• For other streaming websites which solely depend on Flash player, there's that lag you've experienced sometimes. You can do either of these (or combine them):
  1. If you're using Firefox on Windows, you can go to your task manager (ctrl + alt + del) and scroll to Plugin container (Flash on Firefox) then right click on it ► set priority to high. That will reduce the video playing lag.
  2. Try to clear your Firefox stored cache and cookies.
     Click the upper menu: History ► Clear Recent History ► un-tick others but Cookies and Cache ► Clear Now.
     Then stream another video.
  3. If it's still lagging even though you cleared the cookies and cache, try to restart Firefox. Or a bit further, restart your machine. Then try to stream again.
  4. If those steps didn't help, the last resort is to reset (or refresh) your Firefox. You can go to this link
  Remember, you need to also regularly update your Flash player browser add-on.

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The post below is mostly obsolete, but updated on some parts.

It'll be super cool to read only if you're curious.
:)

I'll abbreviate YouTube as YT.

For your information, my internet connection is pretty much sufficient for streaming, ranged around 1 - 4.8 Mbps, near 125 - 600 KBps. I'm using a super neat wireless/mobile 3.5G modem here. So that I can bring it anywhere I want, like a stupidphone.
It's like, 500 MB file download would take a half - 1  hour to finish. Depends on the clouds and thunders, weather, per se. For streaming at other online places, it goes flawlessly.

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Updated
Right, as you've noticed, what happened at YT after Google bought it:

• There's a gigantic advertisement on the homepage (I don't mind about it, sometimes the ad is neat, sometimes).
• The layout and the user interface are drastically changed (which pissed off a lot of users and creators for some reasons. Mainly because the old YT-front-face was neater, and partners could really craft their channels to be unique and sophisticated back then).
• There's that super sweet algorithm for mobile and limited connectivity (new 144p resolution). The default view is "auto", therefore YT can determine what resolution suits your internet connection the best. Like, blur and clear, and blur then clear, haha.
• You can't stop streaming (not stop button, but stop streaming), like on the old player. On the old player, you can right click the video, and there was the "stop download", and the video would display the thumbnail of it. Now, this feature is eliminated. All you can do is pause, and the stream will also stop altogether, but still cached the earlier buffer. If you click the time slider to certain not-yet-buffered part, with limited internet connection (<1Mbps), 50-50 chance that the video will return "error". Especially on Firefox. On Chrome, well, Chrome is insane. Good insane.
• You can see the "stats for nerd" of the video, which is sumthin new.
• The player is equipped with 3D view if the video is made with 3D FX.
• Paid subscription thingy for creators with multiple thousands of subscribers.
• Mandatory "Creators Academy" for users (creators) which got copyright strike(s)/sanction(s). Bwahaha. Ha.
• Free online video enhancer FX. This one is sweet.
• Other thingies you saw at "video manager" or "channel setting", such as free channel promotion and others.
• You MUST have a Google Plus account to create a channel, or just to put your comment on video(s) (but I think Google will like, eliminate that, maybe).
• Your own comment will appear on your video if you share that particular video on Google Plus (kinda weird).
• You can monetize your video even though your channel is just 1 week old (probably). Unlike the earlier YT, the partnership was based on the age of channel, continuous effort of quality upload, and total views. In the old days, being a YT partner was really hard.
• The super new earning system. It's based on frequency of uploads and something something, you can learn it on YT partner documentation or AdSense or other related YT-Google official matters.
• And some others...

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With those simple tweaks, hopefully you can stream any online videos peacefully using Firefox.

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Reference for YouTube with Firefox discussion

This recommendation by R Yuki at
productforums.google.com/forum/#!msg/youtube/1H0GSp21nmw/j86yh3_5hbEJ

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Updated Feb 16, 2015