Acrostic
An acrostic is a piece of writing in which the first letter of each line, read downwards in order, spells out a word, a name or a message.
The form is ancient. Several of the Hebrew Psalms are alphabetical acrostics, with each verse beginning at the next letter of the alphabet, and Edgar Allan Poe hid a woman's name down the opening letters of a valentine poem. Because the hidden text is carried by the layout rather than the sense, an acrostic reads perfectly normally to anyone not looking for it.
As a puzzle rather than a poem, an acrostic gives you a set of clues whose answers, stacked in order, spell a further word or phrase down their initials. Solvers use the emerging vertical message as a hint for the clues they have not cracked yet, so the puzzle tightens as it goes.
Two relatives use a different column. A telestich hides its message in the last letters of each line, and a mesostich uses letters from the middle. Where a poem carries an acrostic, it is most often a dedication to the person the poem is really for.
Poem of the Day — a new poem every morning — some of the classics carry acrostics.