Süßwassertang (or "suesswassertang") is a plant that people in Europe and North America have been growing in their aquaria for a few years now (the name is German for "freshwater seaweed"). Specimens are propagated vegetatively by simply breaking them apart. I haven't been able to find out exactly where it originally came from - internet fora refer to a probable source from a German botanic garden, but it seems that specimens have mostly been passed around by private individuals (see this discussion, for instance). The original assumption seems to have been that it was some sort of liverwort, like a similar-looking aquarium plant known as Monosolenium tenerum or Pellia* (in fact, Süßwassertang has also been referred to as "round pellia", in reference to its different growth habit from true pellia). However, rarely produced gametangia (reproductive organs) suggested that it may be a fern gametophyte instead, and this has been confirmed by Li et al. through molecular analysis.
*It originally appeared on the market as Pellia, but has since been re-designated Monosolenium tenerum (see here). The Wikipedia page on Monosolenium suggests that this may also be wrong, but doesn't give any sources for this claim. Liverworts are far from easy to identify, so it's not outside the realms of possibility.
Süßwassertang turns out to be very closely related to Lomariopsis lineata in the Lomariopsidaceae, which looks like this (photo by Julie Barcelona):
Lomariopsis lineata is an Asian species of the pantropical epiphytic fern genus Lomariopsis, members of which can climb up trees on long running stems to heights of ten metres (Rouhan et al., 2007). That an arboreal fern could produce an independent gametophyte is surprising - that such a gametophyte should be aquatic is incredible. A number of websites have already started referring to Süßwassertang as Lomariopsis lineata, but this is jumping the gun a little. To date, no Süßwassertang specimens have been successfully induced to produce sporophytes, despite their occassional production of gametangia (normally in ferns, gametophytes produce male and female gametangia, the gametes from which fertilise each other and grow into sporophytes). Even when Süßwassertang were transplanted into terrestrial conditions, no sporophytes were produced though gametangia production increased (on the other hand, their growth was much reduced). Süßwassertang has so far only been demonstrated to be extremely close to L. lineata, not necessarily identical with it.
As alluded to in the previous post, independent gametophytes may be able to survive in conditions which their relevant sporophytes would find intolerable. The Süßwassertang would seem to be one of the ultimate examples.
Li, F.-W., B. C. Tan, V. Buchbender, R. C. Moran, G. Rouhan, C.-N. Wang & D. Quandt. 2009. Identifying a mysterious aquatic fern gametophyte. Plant Systematics and Evolution 281 (1): 77-86.
Rouhan, G., J. G. Hanks, D. McClelland & R. C. Moran. 2007. Preliminary phylogenetic analysis of the fern genus Lomariopsis (Lomariopsidaceae). Brittonia 59 (2): 115-128.