Possibly best known for the song "Oh Susannah," which most of us knew as kids, Susannah's got a lot of history besides that. The original Hebrew version of the name was Shoshana, meaning "lily." This and the Persian version may have roots with the Egyptian word for lotus. This Biblical name was not widely popular until after the 17th century, but was used regularly enough since at least the Middle Ages. The song "Oh, Susannah" was written by Stephen Foster in 1848 and widely associated with the gold rush. (By the way, you can hear one variant form, Shushana, in the movie Inglorious Basterds.)
The spelling including an "h," as opposed to Susanna, was the form used in the Old Testament, the story of a woman was was falsely accused of adultery by two old perverts, found in the book of Daniel and omitted from some texts. On the other hand, the spelling without the "h" is more European. Susan, popularized shortly afterwards, is a vintage-sounding literary gem possibly best known from The Chronicles of Narnia. This variant was in the top 10 for over two decades, Suzanne ranked in and around the top 100 for about three decades, and it might be good to know that Susanna has only been off the charts since 1997, but Susannah has not been in the top 1000 since 1978 and hasn't ranked above #800 since 1880.
Oddly enough, one late namesake is Susannah York, a British actress, which you might remember from the 1978 movie Superman. Also the name of an opera, a Saint Susanna, and the name of one of William Shakespeare's daughters. Other than that, there haven't exactly been any stand-out namesakes. Susannah of the Alamo and some famous daughters, but that's about it.
Potential nicknames: Sue, Susie, Sosie, Sookie, Sukie, Sukey, Sunny, Susa, Sun, Sana, Hanna/h, Anna, Anne, Nana, Nan, Zuzu, Zsu Zsu, Zsa Zsa (and Susie Q if it floats your boat)
Variants: There is a slight possibility that Isannah is a variant (see here) but for sure, variants include Susanna, Susan, Suzanne, Suzannah, Suzette, Susette, Sanne, Zanne, Shoshannah, Shoshana, Zsuzana, Zsuzannah, Shanna, Sosana, Susanka, Sosannah, Sousana (and Azucena is of similar origin, can have most of the same nicknames, and also means "lily"). Chochana is a spelling variant used in France.
Here are all the variants and number of births per name for the different versions used in 2011.