I had an anonymous question asking about hat storage in both dorms and at home. Since I deleted the question completely by accident I am just going to ramble on where a question would normally be.
I am going to assume Anonymous meant ball caps, because that is where my head went when I read the question, and because the easiest solution I found is for ball caps.

Jokari 2 Cap Racks for $7.50.
I actually found this @ a Bed,Bath & Beyond last week and took a photo with my phone to remind me to answer here. I posted about the purse rack similar to this some time ago. The Jokari over the door systems really seem to be just what renters and students need. No special hardware, no high ticket price and completely removable.

This is how caps sit on the cap rack.
As you can see though it is not really an option for hats like fedoras and sunhats…so just in case Anonymous meant hats in general, I kept looking and this is what I found:

Gorgeous vintage collection photo source.
Unfortunately if you are heading to a dorm, or are really worried about security deposits, giant nails in the walls are not really an option though are they?
Also, I should note that 9/10 hat enthusiasts do not recommend this for hats that you intend on keeping and wearing./ Although the tenth says that as long as the hats are rotated to and from hat boxes before and after shifts on the walls they should be fine. Source.
So, if it is not ball caps you are storing, and you can’t hammer giant nails into your walls then what are your options?

Original Chain Gang Toy Organizer - White $9.99
I cannot attest to the pressure marks left by the clips but I think this is a great idea. Hats of all sizes and sorts would fit on this six foot tall ceiling mounted chain. Ten packs of extra clips are available for $6.82.

Traditionally, and ideally hats should be stored in boxes, stuffed with tissue paper. Normally this is not the most practical solution due to size, but thanks to The Container Store you can score these square ones for made from 98% post-consumer recycled paper materials for as low as $4.99 each. Now you just need the shelf space to store them and that I cannot help you with.

Photo Source.
This is the next best thing after a hat box. The hat is able to sit supported even though it is still vulnerable to the elements. These Large Wire Stacking Shelves are readily available on Amazon for $6.99 a piece.
This was a great question, and I am glad I didn’t stop at caps because I did find some ideas I wouldn’t have thought of otherwise. I hope this helps, and as always, please share photos! Cheers,M.