Logic (from the Greek logos, which has a variety of meanings including word, thought, idea, argument, account, reason or principle) is the study of reasoning, or the study of the principles and criteria of valid inference and demonstration.
Go to Google Trends (see resources below). Google Trends is a great way to find most popular searched words on Google. It lists the top 100 searched words and is frequently updated throughout the day. You can click on any of the search words and find out more information about it. Go to Yahoo Buzz.
Re: How to find the most searched keyword in youtube. I don't think there is any program that does that. But it's very likely that a search term that has more searches in google will have more views in youtube. Of course some keywords can't be represented with video.