Actually baby wipes are incredible at removing grease and road grime. Wetwipes (the really thin ones) aren't very good, but baby wipes (the thicker ones) are great. I get the store brand type - nothing fancy.
They are also good for emergency toilet stops in the ditch, for cleaning the sweat and salt away so that you don't develop rashes in uncomfortable places, and if they happen to dry out, they make great tissues that don't dissolve when you blow your nose.
I've been carrying and using them for years ... and I've got a pack in the garage for when I'm working on my bicycles at home ... I actually need to pick more up on Monday.