Go to Google.com, type your search phrase and append the following parameters to your search query: site:youtube.com "watch in normal quality watch in high quality"

Once you've found something you're looking for available in better quality, copy the YouTube URL and swing by KeepVid (or have the bookmarklet handy). Paste in the URL and click the Download button. KeepVid will offer you both the lower-resolution FLV and the higher-resolution MP4 — download the latter to save to your phone for reference when you're lacing up that turducken in the kitchen for Thanksgiving.