Firefox: Everyone's trying to avoid Flash these days, what with its CPU-hogging and battery draining. If you need to watch videos on sites like YouTube or Vimeo, though, you can replace them with lower-power Quicktime and WMV plugins with FlashVideoReplacer.
After installing FlashVideoReplacer in Firefox, any time you go to YouTube, Vimeo or Blip.tv, your videos will stream through a plugin other than Flash (QuickTime on the Mac, QuickTime or Windows Media on Windows, and a slew of other plugins on Linux). Not only will this reduce the strain on your computer, but these plugins are also usually more cooperative than certain Flash video players that can be temperamental (Vimeo). I was surprised at how well it worked on my Mac — just install the extension and watch some videos. They play remarkably smoothly, and you can even choose your preferred YouTube resolution in the extension's settings.
Note that you still need Flash installed for this to work; it just won't use Flash to play the entire video. So you can't use the Gruber method of going completely Flash-free here, though you could still easily use a Flash blocking plugin to block all other sites but those that are compatible with FlashVideoReplacer.
FlashVideoReplacer is a free download, works wherever Firefox does.