if you drive your car normally and take care of it the way Toyota recommends (also found in the owner's manual), you shouldn't have any major problems with your car.
but if you drive the hell out of it and don't follow a regular maintenance schedule - then YES, YOU WILL HAVE PROBLEMS.
The Celica has been around for the past 30 years - I agree that it was time for Toyota to move on. They have something better in the wings
It could be worse... you could be driving a Mitsubishi Eclipse or even a Saturn - how often do you see one of them on the roads compared to the the number of older Honda & Toyota