I push my film around all the time.
I've had good luck with Delta 3200 and DDX. If you do medium format, the grain is hardly there. But, I also second the thought of developing it one stop higher than you shot it. Grain becomes much more apparent with the smaller 35mm.
The reason a lot of folks will push is to have a shutter speed high enough to handhold, obviously, or add contrast to a flat light scene. Usually pushing gives more grain, more contrast because you are underexposing the film (giving less exposure and consequently more blacks) and then developing appropriate time to develop in the highlights. The longer you develop, the more grain usually shows up, and sometimes, the midtones start to go. So, artistically, if that's the look you are going for, then pushing the film is a great thing. Sometimes I've pushed film (400 speed to 1600) in broad daylight, by sticking ND filters or red filters on the lenses, opening up and shooting faster shutter speeds. Especially if your camera maxes out at 1/1000 or less.
I rarely use the 3200 speed films, and prefer to push TriX or HP5.