The occurrence of a 1st-year Slender-billed Curlew at Druridge Bay, Northumberland, UK in May 1998 is widely acknowledged to be one of the most incredible bird records ever. This is due to the rarity of the species, with breeding grounds currently unknown despite extensive searches of suitable habitat, including the areas Siberia where it was last seen in breeding habitat in the 1920's, and wintering records from the last regular site in Morocco having all but dried up.
More information on this record is available for example on the Birdguides website. Recent published articles on the sighting and the Slender-billed Curlew in general, include:
NB - despite a meticulously documented review process (cf. articles 1-3), the identity of the bird in question is still contested by some. Some disputed whether one of the plates in the first article listed (plate 164) really shows the bird in question (see recent discussion on Surfbirds mailing list) but a response posted by BBRC seems now to have settled this.
Not taking anything away from the record, I have not given it top spot in my personal "incredible birds" rankings because given the continuing survival of the species, the UK is not that strange a place to find a vagrant Siberian-breeding wader. Nevertheless, if the species does become extinct the fact that one of the last sightings should be here in the UK is almost beyond belief, and I might be tempted to re-order my list!