Well, I can't measure up to some of the posts here, so I'll put a few things out that sets me apart from most geeks:
I have no interest in video games. Period.
I'd rather swallow molten glass than watch Babylon 5, Dr. Who, Buffy, or Angel.
I don't have the rules to any version of D&D memorized. I know where to find what I want and I wing the rest and my players love it.
I have rudely turned my back and walked away from someone in a game store who felt it necessary to tell me about their campaigns or their munckin-a$$ed characters.
I'm sure there are more, but the painkillers in my system slow down the thinking processes.
Here are some things that would qualify me for geekdom, or at least qualify as my quirks. I think geekiness is completely subjective, however, and one man's geek is another man's eccentricity
I love paleontology. I've read pretty hard core books on the subject, and will stop whatever I'm doing to read or watch something on the ancient past. I greet every new paleontological discovery with the same glee a child greets Christmas morning. I got into a shouting match with a paleontologist at the Denver museum over what time period the Morrison Formation existed in, and was justified when a guide pointed out I was right. A friend of mine knows Robert Bakker personally, and has vowed to never let me in the same room with him because he doesn't want to see us argue over Bakker's theory that Ceratosaurs were swimmers. I think he's gone round the bend on that one.
Regarding the historical era, anything that happens after 1400 AD is a current event.
I love the Star Trek universe. While I've been highly disappointed with Enterprise (and just as it was finally GOOD it gets canned), I still love the setting(s). I don't read the novels, but I cherish the technical books and Star Trek "history". I still own my first edition Starfleet Technical manual and Enterprise blueprints that I've had since I was a kid (both first printings and in near mint condition, I might add).
I obsess over my gaming dice. I have every die I've ever owned, except for ones I traded away for another complete set or gave as a gift. I've never lost a single die in nearly 20 years of gaming.
I obsess over my Dragon Magazines. I have every issue from #113 onward, and nearly all of the ones prior to that one. As many of you who subscribe are aware, Paizo's printing company has problems getting issues to some of us on time. I have the customer service number memorized, and in this year alone I've had to use it 6 times to get replacement copies of issues that NEVER arrived at my mailbox.
I love 80's heavy metal. Not the Bon Jovi or Poison metal, but true metal like Manowar, Iron Maiden, Judas Priest, Virgin Steele, or Dio. I have created adventures based on their lyrics, and some of those have been the best games I ever ran.
I think jumping spiders rock. The other families of spiders I don't care about at all, but I have followed a jumping spider across a field on my hands and knees observing its behavior.
I'm sure there are many, many more things, but writing this took nearly an hour as the Vicodin made its merry way across my pain receptors and slowed my synaptic processes.
Geek on.