The classic example is the "Fail Whale" on twitter. But I'm interested in what people's thoughts are on this.
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WRT a 503 and "best user experience" ... it's rather ironic question isn't it? But for best experience for the user, information is king.
So, make sure to include some information for them about where they can find further info -- a link to your status page for example. And then of course, make sure that information about what is happening, and when it will be fixed.
As far as the "fail whale" being a classic ... that's because it was seen so often.
As far as best user experience, I suppose the whale is entertaining. I have seen many funny 404 and 503 pages. Entertainment and information are the key in error reporting, imho.