I would like:
-straight or almost straight fork with a lugged crown
-chromed or accented lugs
-small diameter tubes
-beautiful dropouts
-close tyre clearance
-high bottom bracket
-threaded headset
-horizontal top tube
-geometry between an aggresive roadbike and track
-no brake cable routing
-decent sizes e.g something in the 63cm region

I like familyman's suggestion of being able to customise things like bottle cage mounts etc. For specific urban fixie I'd want none, but for a winter training fixie I'd want one and I'd also want mudguards and a more relaxed geometry.