ALL airliners are designed so there is downforce generated by the horizontal stabilizer in flight.
ALL commercially produced General Aviation aircraft that have horizontal tailplanes are designed so there is downforce generated by the horizontal stabilizer in flight.
Airplanes with canards may not have any downforce produced by a rear horizontal stabilizer (or may not have a rear horizontal stabilizer at all). Those that do not have rear horizontal stabilizers are typically designed so the canard will stall before the wing in most flight regimes (e.g., Vari-Eze).
Some Fly-by-wire military airplanes may fly without downforce on the horizontal stabilizer in some normal flight regimes (e.g., F-16).