$1 or less..
As a college student, I do not have terribly much spare cash. Therefore, I like to keep as much of my money invested as possible, or at least in a savings account earning double the interest of my checking account.
I track all of my finances in Gnucash, where I also account for all future bills coming out of any particular account. I also have free overdraft protection, though I have never needed to use it. Lastly, I put all of my irregular (non-bill) expenses on a rewards credit card that I always pay off by the end of the month. This means that when I say it is at $1, it could easily mean $1+Rent+Utilities, but $1 will be the final value when all the bills go through.
Since I micromanage my accounts effectively, I feel safe with between $0.10 and $1 in any particular checking account. However, as I continue to work I will likely be moving my zero balance upwards, first to $10, and eventually likely up to $200 or so. However, I believe that with my temperament I will never see a need for a particularly large checking type account balance outside of a temporary event such as buying a house.