I can't think of any specific items, but I'm sure that with all the tunneling work for the Underground in its 140 or so years' history that there must have been a good many interesting finds. Sometimes things have been uncovered which the tunnelers would rather not have found. There are several places where right behind a tunnel wall is an old "Plague Pit" from the 17th century, and in fact a tunneling machine digging for the new Victoria Line in the 1960s plowed straight into one (somewhere around Green Park).
Treasures were deliberately stored underground during World War II. The Aldwych branch of the Piccadilly line was closed for the duration and the tunnels used to house all sorts of valuable material from the British Museum.
Speaking of Aldwych (closed since 1994), it's one of many stations which is reputed to be haunted. It was built on the site of a former theatre, and is supposedly visited by the ghost of an actress. Covent Garden also has a theatrical ghost, an actor who was killed outside the Adelphi Theatre in The Strand in the late 19th century and has been seen walking the platforms in top hot, tails, and evening wear. Bank station's ghost is supposed to be a nun. There are many others.