This actually happened to our Teen Librarian, but it was too weird to not include it...

This man came into the children's department, bearing the distinct stench of alcohol-soaked clothes, with a bag tucked closely against his side, and approached the librarian. "Do you have any books on ducks?" Being the excellent librarian that she was, she asked if he wanted fiction or nonfiction, and for what kind of duck.

"Like this kind!" Out from the bag he pulled a full sized living duck and set him on her desk! Needless to say, Duckman was asked to remove the duck and to leave the building. He did come back many times, permeated in alcohol and often accompanied by an animal friend. Neither Duckman nor the animals were welcomed back.

Serpentine Poet

For a period of about a year I had a very friendly stalker, the long-lost twin of Axl Rose (Guns N Roses, c'mon guys!). Axl had a disability of sorts that caused him to walk with a cane. One day he caught me alone at the circulation desk and graced me with his bodacious poetry...for three hours!

Afterwards I told my boss, whose only advice was to "look busy" everytime he came in. Axl wasn't fooled by it; he knew I couldn't resist his turn of phrase.