This is an interesting subject to me. I can ride all my bikes without hands, but I find that the geometry and weight distribution are the biggest factors. I will second what Road Fan said about race geo frames. On my Univega, I can only ride no hands well at high speeds and/or by sitting all the way up and reclining slightly. Even then, it's not especially confidence inspiring, I usually only do it to get a drink or get something out of my pocket/backpack, adjust brakes, etc. However, though my Colnago has lightning fast turn in, it's rock solid with no hands. It can be ridden at crawl, fast, turning, going over bumps, do a U-turn... Heck, it can even do all that while pedaling, with no hands!