If you copy text that is styled, like from a Web page, and then paste it, you will get the style as well. If you just want to paste the text, use Edit, Paste and Match Style in TextEdit and Pages. In Word, use Edit, Paste Special.
Related: Copy & Paste From Safari to MS Word, Copy and Paste Locations in iPhoto, Copy and Paste Files, TextEdit Favorite Styles, Set TextEdit As Default App to Open Word Docs.

Thankyouuuu! that was the most annoying thing ever, inserting a bunch of tabs and hyphens in my plain text