Depends on the frame and the materials used. My steel expedition tourer is the stiffest bike I own, but it is a heavyweight built for load-carrying. Generally speaking, light+stiff = expensive, but still not especially pricey compared with good carbon frames. And a degree of flex is a good thing, of course - laterally stiff but vertically compliant, as they say.

I'm taking it you want a road bike. I have a Kona steel frame - it's a single speed, as it happens, but I believe it is the same tubing as they use for their geared road bike - which isn't the lightest frame I have ever had, but is plenty stiff enough for me, a 200lb rider. Getting more specific, if you look on e Reynolds and Columbus websites you'll get a lot of technical information about the characteristics of different tubing. Some of the more notable UK frame builders use Reynolds 853 for their top-of-the-range road bikes.