Ah, so it seems that in 4E, ability checks are seen as the exception rather than the rule. Does that about capture it?
Follow up question: In 3E, is it possible to make a non-proficient skill check?
I would say ability checks are the exception D&D 4e. It was true in my experience and the Rules Compendium actually says that DMs can differ on whether a Strength check or an Athletics check is appropriate (for example). I think it's probably safe to say most DMs would call for Athletics.
Despite playing D&D 3.Xe for 8 years, I do not recall very much about the rules so I can't answer your second question.