"Sunshyne," originally by Cream, by Thousand Foot Krutch.
"Unbelievable," originally by EMF, by Thousand Foot Krutch.
"Carry On My Wayward Son," originally by Kansas, and "So Help Me God," originally by dc Talk, by The Showdown.
"The Promise," originally by When In Rome, by Anberlin.
"Right Here Waiting," originally by Richard Marx, by And Then There Were None.
"Snap Your Fingers, Snap Your Neck," originally by Prong, by Demon Hunter.
"Beggin'," originally by The Four Seasons, by Madcon.
"Life Is A Highway," originally by Tom Cochrane, by Rascal Flatts.
"Peace of Mind," originally by Boston, by Stryper.
Remember, these aren't covers I necessarily prefer to the originals, just that I like. Also, "Beat It" by Fall Out Boy isn't bad.
EDIT: Oh, and I do have a lot more that I like than this, I'm just not posting everything I could possibly go and dig up.