Is it normal to feel like gagging when brushing your teeth?

Not really: You should be able to brush your teeth without feeling like gagging. You may be using the wrong technique to brush if this is occurring. However, you may also have a very sensitive gag reflex, in which case, for you, it would be normal to feel like gagging when brushing. See you dentist to have him or her test your gag reflex and see if there is a way to desensitize it.

Not usually: Occasionally this may happen if you are congested, or have a cold, but it should not happen on a regular basis. You need to ask yourself - when did this start, and what else if anything changed at that time (new brand of tooth paste, eating different foods, etc.). If nothing stands out, i would have an evaluation by your physician or an ear, nose and throat specialist.