Visible noise will always be more visible on screen vs on print. The trick is to always try to use as low an ISO number as possible. I will play with aperture and speed and artificial light (flash, room lights, etc...), before I touch ISO (just speaking in general... there are times I play only with ISO for effect).
If you have unwanted noise (yes there are times noise is good!), NeatImage or NoiseNinja are there just for that.
I know a handful of higher end Wedding Photographers who don't hesitate to shoot at ISO 800 or even 1600. They say that it's not really that noisy if you expose properly. If your exposure isn't great, the noise will show up more and any processing will really bring it out.