It kind of depends on what you are shooting doesn't it?
Even with 35mm if I am shooting something static I prefer to use a tripod or a bean bag etc.. If I don't then I will usually shoot at a much higher speed and also take a couple extra shots just in case. It sometimes works but I have often been sorry I didn't take the time to set up the tripod.
If shooting a bike race or kids party I don't usually use a tripod but I am also not expecting big enlargements. I have gotten some great results shooting mountain bike jumps or football games with a 300mm on a monopod, but some movement blurring is to be expected.
When shooting with strobes I often don't as the speed of the strobe will take care of any camera shake and it gives me a little more freedom with 35mm or medium format.
Of course with 4x5 I always use a tripod as I'm not tough enough to do it hand held even if I wanted to.