Do your tellers take their teller drawer keys home with them each night? Where are the extra keys to each teller drawer kept?

NO! They are locked in the vault under dual control.

For the last 12 years I worked at banks where our tellers were responsible for their keys and therefore took them home each night. Extra sets of keys were kept in a fire proof cabinet and/or vault under dual control. I can not recall one incident where we had an issue.

The way banks experience teller turnover around here, it's not worth having them take the keys home.

I've worked for banks for over 20 yrs. Including several large banks. The tellers always kept their keys. Some would leave all but a few in their cash drawer overnight, but that was their choice not a policy. Don't believe I ever heard about any problems.

I haven't worked for banks for as long (only six years), but I have seen some things happen when tellers take home those keys.
On three different occasions at my last bank, the tellers made copies of them and then used the copies to get into other people's cashboxes.
I guess that's just one scenario I thought of off the top of my head that could be a problem (I know it's not the norm, but it did happen...)

Our tellers have been assigned the authority and responsibility over their teller drawer keys and take these keys with them when they leave the branch for the night. Spare teller drawer keys are locked under dual control in the key box.