I know of no airplane that has NO predeparture checklist.
On an airliner, depending on the airplane, the checklists can be fairly simple or quite complex, generally depending on the presence or absence of automation.
Older technology airplanes (DC9 MD80, early 737) have few automated systems, so there are a lot of switches to check and readings to confirm, so their checklists are "busy" and long.
FYI, our MD80 has about 15 items that are checked in the gate, and about another 10 that are checked after the engines are running and before takeoff. Each airline develops its own checklists, using the manufacturer's checklists as a guide.
Newer technology airplanes (B757, 767, 777, Airbus) are more automated and their checklists are much simpler. A 757 checklist may have fewer than a dozen items from "cold dark airplane" to "ready for takeoff"
No runup is done, but a "health check" is done as power is advanced for takeoff. An engine power setting is calculated for takeoff, and if the engine meets the required power without exceeding temperature or speed limitations, the takeoff continues. If not, the takeoff is aborted and the reason determined.
A full power engine run is done periodically by maintenance folks to confirm the engine's health.