"Your name's Geek? Do you know the origin of the term? A geek is someone who bites the heads off chickens at a circus. I would never let you suck my dick with a name like Geek."
Well, it's more specific than just 'troper'. Most Tropers Are Young Nerds and/or Geeks, however, so in a word–yes, us. Of course, where any given troper lies on the scale of geekitude depends what one considers a geek/nerd in the first place. To wit–the distinctions between "geek" and "Nerd" are many and various, or maybe there aren't any distinctions at all between them. It all depends on who is using the term.
For the record, geek is an old Carny term for a species of sideshow performer: a specialist in the art of eating disgusting things (emphasis here on "specialist"). Biting off the heads of live chickens was the classic play. The term entered the popular media through Professional Wrestler Classy Freddie Blassie's 1975 rendition of the charming Pete Cicero-Martin Margulies novelty song "Pencil-Neck Geek".
Somewhere along the line, certain communities–notably info-tech communities–picked up the term as a synonym for "specialist". "He's an Emacs geek," for example, would mean he knows a lot about Emacs.
Another concept of a geek–someone more interested in books or computers than social activities–as also being a Nerd–a person who doesn't "get" social activities at all–was turned on its ear when geeks started becoming everyone else's boss after college. (See: Microsoft, Apple, Google, etc.)
There can be such a thing as a Fashion Geek, someone who knows a lot about fashion and is pretty obsessed with it. A Fashion Nerd, in contrast, would be completely unaware that stripes and plaids are unmix-y, and wouldn't care, even if you told them why the two don't mix.
The show Beauty and the Geek, from some viewpoints, misuses the term, as it focuses in on the Nerd aspect that geeks sometimes display. Still, it can be forgiven because the title's pun doesn't work with "nerd". (Though it is called Beauty And The Nerd in countries where the word "geek" hasn't been adapted into the language.)
Otaku is basically a Japanese synonym (with the same confusion with Nerd), except that in the U.S. it mainly refers to those geeks interested in Anime and Manga, and in Japan it's largely used as a pejorative. A very serious pejorative.
A Geek Hierarchy was allegedly discovered for the first time in 2002 on the Brunching Shuttlecocks humor site.