What are the crystals that have formed around the top of a conc. nitric acid bottle?
Chemicals cupboard often produce quite extraordinary reactions, much like hospitals are home to some unusual and severe infections.

Nitric acid does not normally exhibit such a bizarre behavior. Yet in your case it did. How so? My bet is on some unknown additional component which came from the same cupboard, but from a different bottle. For instance, it could be some lower aliphatic amine (Upd. or simply ammonia, as was brought to my attention by other answers). They are volatile, and they produce crystalline salts when they meet with strong acids.

A similar thing is known to happen with $\ce{NH3}$ and $\ce{HCl}$:  if they are stored nearby, especially in poorly corked bottles, they both (as well as everything around) get covered in a white residue of $\ce{NH4Cl}$. It doesn't form nice crystals, though; it looks more like a layer of hoarfrost. But that doesn't mean much. Related compounds do not necessarily have related crystal structures, let alone related crystal shapes, so it looks perfectly plausible to me that (substituted or not) ammonia nitrate would grow into fine needles.

The prevalence of amine/ammonia in the air within the cupboard (which could happen if the other bottle was corked worse than this one) would naturally lead to $\ce{HNO3}$ molecules fighting this battle at their own doorstep, that is, at the very bottleneck of this bottle and nowhere else. This would explain the accumulation of residue at one spot.