I suppose it depends on the circumstance. I built something for an event at my company on Monday that utilized the Foursquare API to grab recent checkins at the event and make a "slot machine" that randomly picked a winner.
And, you may remember, Foursquare was down pretty much all day Monday. It was an extra thing for the event that I did after hours, a bit reluctant to be spending precious weekend time building it, but I figured it would be worth it. It wasn't.
Obviously, we should have used more than just Foursquare, aggregating checkins across multiple services — I mean, the event was about social media — but unfortunately there wasn't anymore time to do so.
I suppose the truth of the matter is that you shouldn't rely on any third-party service (especially free ones... Facebook and your ever-changing API, I'm looking at you).
Now if we could just get our clients to understand that.