There's nothing scary about breaking one spoke. Your wheel should still remain fairly true and you should still be able to ride quite a distance with one broken spoke. If you break two at one time, you might need to release the brake because your wheel won't likely remain true ... and you should try to replace them soonish.

If you start having a series of broken spokes, you might want to consider new rims. Things wear out over time. It happens. If your rim and spoke are from 1989, it wasn't likely a manufacturing defect, it was likely just worn out.

A couple ways to help prevent broken spokes are to keep your wheel absolutely true, and to avoid potholes.