Rain Room by Random International, an installation of falling water that parts (more or less) as you walk through it, has been very popular with queues reaching up to four hours on weekends. It's eerie and beautiful and slightly damp; to get a better feel, watch this video that James Trosh has put together. You only have two more weeks to experience this in person – the water dries up on 3 March.
Rain Room is at The Curve in the Barbican, daily 11am-8pm, open til 10pm on Thursdays. Last admission to the queue around three hours before closing. Completely free.