The two normal causes for the brake light in the dash to come on (on most vehicles) are low brake fluid or a faulty parking brake switch.
If it's a low fluid situation, topping off the fluid generally alleviates the situation but points to one of two things. Either the pads/shoes are thin and need of replacing or there's a leak in the system.
Leaks can occur in the seals of the pistons and aren't noticeable unless you pull the wheels off and inspect the calipers.
If the parking brake switch is faulty, then it may be something as simple as something having gotten stuck between the lever and switch, depressing the switch. Something more complicated is the switch wire being shorted to ground somewhere as a ground signal is what activates the light in the dash.
What you're describing leads me to believe it's a leak or very worn out pads. Have a free brake check done at any local shop and go from there.