Since a lot of people here are first time fans or have just started watching Everton, I started looking for a place where there were clips of past Everton games. I thought this would be a good way for new fans to get familiar with the club, our fans, and our opponents.
Luckily, I found a website that have highlights for 20 matches from the past season! What's even better is that they have the legal rights to these clips, so you don't need to worry about the site going down. There is one problem though, and that is that, only people residing in the US can watch these clips (I think). Most of the new fans are from here anyway, so it shouldn't be a problem. If the website doesn't work for you - just keep that in mind.
I don't think they are in any particular order.