Have you ever been to a gig and found the supporting band to be more entertaining than the headline act? It's an experience that is somehow disappointing and rewarding at the same time; you leave cursing the main event for being a let down while still being grateful that the whole thing wasn't a waste of time. it's a feeling movie-goers know all too well.
Sub-plots are an essential part of storytelling in all its forms, used to add extra dimensions to the world and to make the characters that inhabit that world seem all the more real. They exist to balance the main plot, providing comic relief if the narrative is intense or romance where there is an overload of action. In short, sub-plots are there to make the main story better, though sometimes they only succeed in making it look worse.
A strong sub-plot (or a B-story, to use the industry vernacular) is a blessing for a movie that has a solid main story and can turn a good movie into a great one. The challenge for the filmmaker is making that B-story compliment the main plot without accidentally overshadowing it, though a sub-plot taking the lead over the main plot doesn't necessarily mean that the main story is bad.
Some of the entries on this list are films with weak central stories that were just about rescued by a good sub-plot, while some are films with a strong central story that just wasn't as good as the sub-plot, though they all have one thing in common - the B stories were better than the A ones.