I do a lot of writing for college, and often clip little pieces of text from the web, such as the names of people or long titles of articles rather than typing them out myself. However, with Word, the defult paste is to paste in HTML format, with whatever style, color, etc. the text is in the website. But I don't want the text to be that way, and now have to either manually change it, or go to Paste Special and choose "Unformatted Text".

I remember there was a way to change the defult paste in Word, but I forgot how. So, how do I make it so the defult paste is Unformatted Text, so I don't have to do Paste Special for my copying?

You can't. You'll have to live with the "Edit", "Paste Special" function. There's not even a registry hack that I could find to do it.