Focal Length — Longer focal lengths magnify camera shake. The reciprocal rule (1/focal length) is the starting point for determining minimum shutter speed.
Image Stabilization — OIS (lens-based) typically provides 2-4 stops of benefit. IBIS (body-based) provides 3-5 stops. Combined OIS+IBIS can achieve 5-7 stops on some systems.
Subject Motion — Still subjects require only enough speed to counter camera shake. Moving subjects need faster speeds regardless of stabilization: walking (~1/125s), running (~1/500s), vehicles (~1/1000s+).
Sensor Size (Crop Factor) — Crop-sensor cameras effectively multiply the focal length for the reciprocal rule. A 50mm lens on a 1.5x crop behaves like 75mm, so you need at least 1/75s.