Free accounts can't get hat drops.
As I recall, you upgraded to a Premium account (and gave @badp
the Professor Speks... jealous ), though.
There are 3 drop timers: Items.
Standard is 6-8 a week, assuming you play at least 6 hours a week.
Note:
To my knowledge, paints and tags are part of this timer, but they have a lower chance of dropping.
Immediately following an update, Valve tends to raise the drop rate for those items.
Right now, you're guaranteed to get 1 Uber-update weapon a week minimum.
Crates.
Standard is around one a week (sometimes two), assuming you play at least 6 hours a week.
Hats/Misc.
Standard is one every 1-6 months, assuming you play at least 6 hours a week.
The length of time that counts towards your next drop is limited to (iirc) 6 hours per week, but if you don't play for a week, the next week will be limited to 12 hours.
Hat drop rates vary wildly.
I've had an 8 month stretch with no hat
drops before, but more recently, I've been getting a hat every 1-2 months.
Side Note: The hat drop rate is bugged during the rare Double Drop rate week.
While the first hat drops at the normal rate, the second uses a much, much shorter timer (the crate timer?).
So, it's not unusual to get two hat drops during a double drop rate week.
gaming.stackexchange.com/users/None/
It's totally random, but very, very rare (for many people).
I get one hat in every couple of months.
(I did receive an Ol' Geezer the other day, but the last time I got a random hat drop was five months ago...)
gaming.stackexchange.com/users/7364/BoltClock
Yes, hats are dropped similarly to weapons.
However, little is known about the drop rate for hats.
For weapons, there is a rate of roughly 8-10 items per week, if you play an average amount of time.
However, hats (and paint, tags etc) are on a completely different kind of timer, where once you find one it can take months before you find a new one.
In my years of owning the game (so suffice since drops were implemented), I've only found two items on the hat-timer.
gaming.stackexchange.com/users/None/
These posts seem out of date after a whole year, I have been playing TF2 for well over 600hrs and have had 1 hat drop for me, at least that's what I thought
but it ended up being a achievement reward.
So, no, I haven't found anything in drops except weapons and crates, no hats nor any unusual items.
gaming.stackexchange.com/users/30882/Ken Smith
I've been premium for less than a week, and I've gotten 2 hat drops.
gaming.stackexchange.com/users/38200/Hale
The chances are really low, but it's like the drop system; I didn't play for months, and after I started again, on my first drop I got a Brown Bomber.
gaming.stackexchange.com/users/38719/Random answer
I think I read somewhere that with a premium account you could get hats in drops as well as weapons. I have now 50 hours of premium gameplay, and I never received one.  Was I mistaken? Or are the odds really low?
Can I get hats in random drops?
gaming.stackexchange.com
<team-fortress-2>
gaming.stackexchange.com/questions/27867
gaming.stackexchange.com/users/14/juan
It's not unusual to get two hat drops in a double drop rate week. Hats are dropped similarly to weapons. Little is known about the drop rate.  Hats can be obtained in drops. However, this is rather rare and random.
The length of time that counts towards your next drop is limited to (iirc) 6 hours per week, but if you don't play for a week, the next week will be limited to 12 hours.
The rate of a hat drop varies.