Clare is the second oldest college in Cambridge after Peterhouse, founded in 1326, although it doesn't look it from the river as the buildings you can see from here were built in the 17th and 18th centuries.
What it's particularly famous for it its bridge. Clare Bridge is the oldest surviving bridge over the Cam and it has 14 stone balls along the top. 13 of these balls are intact but one has a wedge missing. One of the stories about this is that when the stonemason built the bridge, Clare didn't pay him enough so to spite them he took a slice out of the ball and took it away to even up his payment. Although this is a good story, the probable explanation is that the ball was repaired at some time in the past. It may have become loose on the metal rod holding it to the bridge, so a wedge would have been cut out to release the ball, then the ball turned on its side and a new hole drilled to re-fix it. The cut out wedge would have been filled with another piece of stone that since then must have fallen out and is presumably somehwere at the bottom of the river!