It depends on where you live of course, but if you take the UK, the best known night bird is the owl (though it doesn't exactly sing.) Otherwise, the night birds to listen for are the nightingale, the nightjar and the corncrake, mainly in the spring and early summer. You can soon learn to identify these birds if there are any near you - you can listen to recordings until you're familiar with the sound and then try and hear them outside. The loveliest song of all is the nightingale.

Other birds are often active at night too, especially the robin - it's not a nocturnal bird but is very light sensitive, and will sometimes wake up and start singing even if there is just a street light nearby. Some warblers also sing at night, though again they are really day birds.

You can learn more from the RSPB website.