You can keep it for a few days in the fridge. I would probably go ahead and cook it up and then have quick breakfasts with the pancakes. Just like the frozen ones in the grocery stores, you can just pop them in the microwave or oven, warm them up, and eat.
Years ago I had a roommate who'd do just that. He'd freeze the pancakes (or waffles) and store them plastic bags, and then heat 'em when he wanted a quick breakfast or a snack. That would be my choice for the extra batter as the frozen, finiahed product will keep longer than just the batter in the fridge.
I have to agree with Phill on this one. The reason is that pancakes get their rise from the chemical reaction between and base (the baking soda) and the acid (usually lactic acid in milk or buttermilk.)
After a short time, the acid and base have neutralized and you won't get any rise at all.
I cook them all, and just freeze or fridge the extras and pop them in the toaster to heat up.