Just a while ago I learned the easiest way to copy videos from Youtube to my iPhone. Now I'm sharing it to you.
This procedure is based on my current setup: Firefox browser, iTunes with iPhone connected using USB cable.
1. Download Real Player SP from realplayer.com. Run and install it.
2. Go to YouTube and choose the video would like to copy to iPhone.
3. You will see "Download this video" on the upper right corner of the video when you put your mouse over the video. If you don't see it, it means your Real Player SP is not installed properly.
4. Click "Download this video" button. Real Player SP Downloader window will appear and download starts.
5. Monitor until download is finished.
6. When download is finished, put your mouse over the downloaded video and click "Copy to iPhone" button.
7. Real Player Converter will appear and it is converting the video to mp4.
8. Once conversion is finished, Real Player will add it iTunes.
9. From iTunes, highlight your iPhone in the device list. Then click Sync button.
10. Now disconnect your iPhone and go to iPod and search for the video.
11. Click the video and watching.