My wall mounted replica sword that Bilbo gives to Frodo in the Fellowship of the Ring. Either that or the home videos of me sitting in front of the TV with the sound turned down saying every characters' lines in Star Wars when I was 6.
ummmm....I have 11 Pinkie Pies, no wait 13. There is also the Time Turner, Snitch, and a replica of Frodo's sword.
I guess it would depend on the type of nerd...
But for me, I think it would be things I made:
I painted a large (maybe 2 1/2 ft by 4 ft) acrylic painting of Beleg's death (from The Silmarillion/The Children of Hurin)
I am writing a literary-ish essay about Doctor Who (now 30 pages single spaced).
hmm. i have a quill i got from my brother, a plush fred weasley doll, and an assortment of nerdy posters. and i have a mini plush tardis.
What does a mini plush tardis look like? I can't quite imagine it.
The nerdist thing I own is probably my oboe wich I got through band or my doctor who t-shirt or my mocking jay pin
My homemade blue Voy/DS9-era star trek uniform, which has been worn in public exactly three times (NYE '09/10, Halloween '10 and Gaelcon '11) along with trill paint to be Jadzia Dax. :)
Competing with that would probably be a piece of paper with a chibi-thulu drawing by John Kovalic, signed, with the comment "I went to Warpcon and all I got was this Chibithulu sketch!" It has a bonus (chibithulu won't attack the owner of this sketch, honest) and I got it laminated too. He guards my dice. Mostly, I got this by asking. John Kovalic is such an institution at Warpcon that there's a running joke that anything you can take away from the Con that *hasn't* been signed by him is probably worth more.
um, probably my Harry Potter book in hebrew... i made my friend get it for me as a bat mitzvah present...
or maybe my hedwig, bertie bots, snitch, time turner, mockingjay, and mirror of erised necklaces and sorting hat earrings...
I'm proud to admit that I own a legit piece of the Berlin Wall! ...and that I totally brought it to every history class I had in high school. I got it from a friend of my mom who was in Berlin at the time the wall fell. However, since the wall fell in 1991 and I was only a tiny baby, my mom held on to it until I was a freshman in high school. I will never know why she waited so long to give it to me :/
I also own a replica of a WWII Nazi Germany sword... but I don't remember what division of their military that it's from. I got it as a graduation present from the "alternative to college" program that I went to - where the tradition is to give out a sword after three years of completing the program. I have a fascination with Nazi Germany (in a healthy, pro-awesome, anti-world suck kinda way) and that was the sword my director decided to give me.
Finally, I have an extensive library of Nazi Germany documentaries and books that were acquired numerous different ways.
EDIT: Because I forgot about my other super nerdy item... which I happen to be wearing! It is a shirt that is written almost entirely in chemistry terms :D it says: "We few, we happy few - we band of brothers. For he today that shed his blood with me shall be my brother." (except there's a whole bunch of awesome chemistry stuff on it, I'm just not gonna try to recreate it) Then, on the right sleeve, it has a list of all the Cations (positive ions) with their IUPAC Name/Symbol; on the left sleeve, it has all the Anions (negative ions) with their IUPAC Names/Symbols. The back has everyone who took accelerated chemistry in '07-'08 with their nickname. (I was fortunately named Brittany, so I got Brittany Spears... yay me) I have this shirt because I took the class and forked out the $25 to be a nerdfighter before I even knew what a nerdfighter was!
Probably all my electronics books and tools.
The art of electronics is a great book
I also have a few multi-meters and a soldering station.
Also all of the projects I have made.
Various nerdy electronics t-shirts.
Oh and an xkcd poster.
Probably my Aristotle and Socrates bookends... or my 120-ish pigs (piggy-banks, stuffed animals,that sort of thing). No I'll go with the bookends.