I'm getting water in my furnace when running my air conditioner. What could be the problem?

It could be an iced coil or plugged drain, cracked condensate pan, rusted out pan, you will have to shut it down and remove the front panel and see if the drain is plugged or get an idea where the water is coming from.
Some times if the filter is not changed on a regular basis the evaporator coil will get dirty and cause iceing, the best way to clean this is to disassemble and take outside and wash with a hose. Now the fun part is that sometimes you can't remove the coil without removing the furnace first, this said it can become a labor intensive job and costly.

If you take coil out, you in a heap of trouble,, never do that there are spray chemicals that are safe to spray on coil to clean it where it sits,, check the other possilitys first, stopped up drain,cracked or rusted pan,, taking coil out means calling out the a/c man to get you $$