Kazan is unlike anywhere else in Russia, so be sure to pick up a traditional souvenir or three in order to remind you of what we can only hope is a glorious time in the Tatar capital. Traditional clothing is always a winner, but the old male headdress in these parts deserves extra attention. Men absolutely should purchase a tubetey, but be ready to shell out a bit of money for a genuine one unless you want to go home with a cheap knock-off. If headwear isn’t your type of thing, get yourself a pair of fantastic Tatar boots.
The Islamic population in Russia is largely forgotten, and Muslims make up 55% of the Tatar population. Unique Muslim Tatar designs are a fantastic choice of souvenir in that case, whether it is special versions of the Koran or something a little less intense. 
If all else fails, Kazan cats are famous souvenirs from the region. Check out the cat monument while you are in town for more on that.