It is possible, theoretically speaking. If you had a regulator able to handle a huge range of input voltages, then you can start at the top of the range and have it regulate all the way to the bottom of the range.
e.g. If you have a regulator that can handle max Vin 9V and min Vin 0.6V, you can have 6x1.5V batteries. That would give you 9V input. When they run down below the min Vin of the regulator, they would produce a total of 0.6V, or 0.1V per battery.
You could, theoretically, put together lots of batteries which are close to dying to get a usable voltage, like 15 of those dead batteries at 0.1V each to get your 1.5V.
Practically speaking there are some limitations and considerations. I think one of them is that as the battery discharges, its internal structure breaks down, so your discharged batteries are more prone to leakage. Also, the variations in manufacturing are more apt to show themselves when the batteries are nearly exhausted, which is why in a multi-battery set up, you will sometimes see one battery suddenly die and cause the reverse voltage problem as mentioned by Nerd.