From negative to positive. NOTE: In some electrical/electronic communities, the direction of current flow is recognized as being from positive to negative. ---http://www.tpub.com/neets/book1/chapter1/1n.htm

And it's interesting to realize that the current flows, not the electrons themselves, which move rather slowly, and in alternating current they hardly move at all--just go back and forth 60 times a second. Was it here on Answerbag that I read that current in a wire does not move at the speed of light, but only about three fourths of it? No practical importance, of course, unless you're designing the next-generation computer chip.

As the questioner mentioned 'the Battery.' 'AC' or 'Alternating Current' is not an issue... All 'Cells' or 'Batteries' are 'DC' or 'Direct Current.' & supply the Circuit with a 'EMF' or 'Electro Motive Force' The 'Current' is measured in 'Amperes' & The 'EMF' in 'Volts.' But are You asking about the Current (In) the battery? or (from) the battery? in the curcuit? 'Conventional flow' was taught, and is accepted still... so not to confuse, was later proved incorrect. Conventional flow, within the circuit. Is (As in, leaving the cell from the + & returning to the -. & (in or through) the cell / battery they are shown to flow - to +. With normal bulbs the direction of current is not an issue, but as mentioned in another answer 'LEDs' or 'Light Emiting Diodes' there is an issue, as if they are incorrectly fitted they will not illuminate. on a 12v DC car, the -Neg side of the Battery is connected to the chasis & or metalic Bodywork of the car and many circuits return to the Battery though the chasis. With a multimeter you can place the red probe on the red Pos, terminal of the battery & the black on the Neg, this will show you a Positive reading 12v if you were to reverse the probes, then it would display a -12v.

Why do people have a "snipe" (first anonymous) without supporting or explaining what the mean, are they cleverer that the rest of the human race. Or is it that really just don’t not know the answer.

Perform this simple experiment. Take a 1.5-volt cold cell laboratory battery and construct a simple circuit using two incandescent light bulbs of the same wattage wired in series. Which bulb illuminates? Ask yourself why, and then note to which terminals the bulbs are attached. You may get a clear look at the direction of current flow and be done with this age old question and move on to more constructive issues such a impedance vs. resistance or VRMS or the price of tea in China.

What are actually moving are electrons, which are negatively-charged particles. These flow from the negative terminal to the positive terminal. This is all i can remember right now, however you can go to this site called examville and get the accurate answer, It helped me.