[Wasserpest]

Just as guppies in a cage, you can't keep Orchids under water. They are terrestrial plants, and will just die under water. It might take a little while, but I think it is a bad idea, just like the guppies.

Many Orchids are epiphytes, growing on trees where they can live with extremely little water. They get most of their moisture from precipitation (rainfall and dew). Overwatering is the main cause for folks killing Orchids at home. Otherwise many of them are exceptionally hardy. Keep it natural, keep them on your window sill, not in your planted tank.

 

[Rex Grigg]

You can put a cut rose in a column of water and it will last for a couple of weeks. Doesn't mean you can grow them underwater.

 

[SCMurphy]

There is an aquatic orchid, I brought two home from my trip to Europe. The flower is not as showy as the orchids you are thinking about though.

 

[Daniel*Swords]

There are a couple of aquatic/semiaquatic orchids: Spiranthes odorata - Marsh/Sweetscent Ladies' tresses (U.S.); Spiranthes graminea - Canelo Ladies'-tresses (Arizona, Mexico, Honduras, Nicaragua); and Habenaria repens - Water-spider orchid (Americas); & possibly some other Habenarias.

 

[Wasserpest]

You guys are talking about Orchids that can live in wet places, like marshes, swamps, whatnot. The OP wants to grow them under water. There are no Orchids that grow under water. They are all terrestrial, even if some can survive with their roots in wet soil.

 

[Daniel*Swords]

Agreed, my answer wasn't really apropos the fist question. But, at least S. odorata has been cultivated in aquaria, with some success, as it's a marshland plant living in the inundation zone. In this, it is like many other plants grown in our aquaria, e.g. some swords come to mind. Here a quote from Flora of North America (emphasis mine):

Flowering Sep--Dec. Cypress and hardwood swamps, marshes, prairies, riverbanks, ditches; 0--300 m; Ala., Ark., Fla., Ga., Ky., La., Md., Miss., N.C., Okla., S.C., Tenn., Tex., Va.

Spiranthes odorata typically occurs in seasonally inundated sites and may bloom while emerging from shallow water.

Regarding Habenaria repens, the same source writes (emphases again mine):

Plants terrestrial or semiaquatic[--].

Flowering primarily summer--fall, sporadically (Apr--Dec). Marshes, wet meadows, bogs, margins of streams, ditches, and ponds; commonly an emergent aquatic in shallow water and in floating mats alone or with other vegetation; 0--100 m; Ala., Ark., Fla., Ga., La., Miss., N.C., Okla., S.C., Tex.; Mexico; West Indies; Central America; South America.

Habenaria repens is remarkable in sometimes being truly aquatic. Often forming floating mats, the plants then are commonly decumbent, at least basally, and new shoots and slender roots arise abundantly from much of the length of the stem. [--]