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 Files, Copy and Paste Locations in iPhoto, How Do I Copy/paste In iOS5 Safari From One Text Window To Next?, TextEdit Favorite Styles.

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