Zimtsterne (Cinnamon Stars): The best Zimtsterne ever are available in the Marktplatz. Enter the Marktplatz from the southwest and pass the giant pyramid bar on your right. The Zimtsterne are a couple of booths down on the left. You can watch them bake them, try a free fresh sample, and even buy the non-star-shaped ends at a small discount. I can't eat them from anywhere else now. We tried to make them at home and that ended badly, too.
Kartoffelpuffer/Reibekuchen (Potato Pancakes): The two stands I know of that sell these are in the Marktplatz and the platz with the ice skating rink on the far east end of the Hauptstrasse. (Why can I never remember the name of this platz!?) The ones in the Marktplatz are better - more crisp, less gummy. They are in the northwest corner, just a ways beyond the delicious Zimtsterne.
Spicy Wurst: In order of spiciness, least to most: Feuerwurst in the Bismarckplatz, Feuerwurst in the Uni-Platz, Teufelswurst in the Marktplatz. In the Marktplatz you can also get some deliciously horrible Kaesespaetzle at the same stand. Yum!!
Nicest Christmas Junk: There's a little ornament and pyramid stand in the Kornmarkt (northwest corner) that has much cuter, sturdier stuff than most other stands selling this sort of thing. In the back section of the Uni-Platz there is another good one (at least there was last year, but I didn't look for it yet this year). The increase in quality is of course accompanied by an increase in price.
Delicious Dried Strawberries: A dried fruit stand in the back section of the Uni-Platz. Free sampling!!
Vegetarian Options: Kaesespaetzle in the Marktplatz at the little Wurst stand next to the giant pyramid. Kartoffelpuffer in the Marktplatz and the ice skating platz. French fries in the Uni-Platz just at the corner where the back and front sections of the platz meet. Crepes and waffles at the platz halfway between Bismarckplatz and Uni-Platz, in Uni-Platz, in Marktplatz, and in the ice-skating platz. Chocolate-covered fruit at the candy stands (everywhere).
Biggest Freaking Crowd: Around the fountain in the Uni-Platz. Madness! Do not arrange to meet your friends here unless you are very tall.
#1 Place to Get Budged in Front of While in Line: Crepe stands. Germans are the most shameless budgers ever. Good luck controlling your fist of death when you catch the smug look on their face when they've gotten away with it, because you're too frustrated to berate them in your second language.
More contributions from locals welcome!