Several species of whales - notably the male Humpback Whales (Megaptera novaeangliae) - engage in so-called 'singing' displays. (The songs were first noted by undersea microphone systems installed to detect the movements of submarines.)

There are numerous hypotheses concerning the nature of humpback song, many of which are not mutually exclusive. The logistical difficulties of studying the behaviour of humpbacks in comparison to songbird's render it challenging, although not impossible."

Journal of Marine Animals and Their Ecology, Vol 1, No 1 [archived]

The hypotheses regarding the 'purpose' of the songs mainly centre around breeding, but no direct evidence of the male's songs affecting females has ever been observed.

Theories include : Attracting females • male-male competition • male-male cooperation • vocal arms race • 'news' dissemination etc etc

Audio recordings are available via 'The Songs of the Humpback Whale'

Note: In addition to the mysteries surrounding the reasons for the songs, the physical ways in which the vocalisations are produced are also unclear. It's known that whales don't exhale during songs, and so the air is somehow being recycled under pressure. Whales also lack 'vocal cords', so it's assumed some other parts of their anatomy are somehow involved in producing the sounds.

See, for example The Anatomical Record, Volume 290, Issue 6 p. 745-759

Also see Whale song pitch declineplugin-autotooltip__plain plugin-autotooltip_bigWhale-song pitch decline

A 2009 paper from the Scripps Institution of Oceanography, published in the journal Endangered Species Research (ESR) described the drop in musical pitch (31%) of songs of the Blue Whale (Balaenoptera musculus) over a period of 50 years or so.