It would depend on the quality of the splitters and the quality of the feed coming into your house. I am using really nice splitters, and throughout this house I've got a regular digital box, an hd box, and 5 analog TV's hooked up and they look fine.
There's no hard, fast answer here. Depends on the RF signal strength delivered by your antenna, cable or satellite receiver.
In an analog system the picture will get noisy if the level drops below a certain point. This is also dependent on the tuner of the TV or other device.
On a digital system you will see "sparklies" and then signal will go away completely.
Unless you have access to a signal strength meter, you can only try it and observe the image for degradation.
I have my digital cable split three times at the outside of the house, one going upstairs, one in the first floor, and one going into the basement. The basement wiring gets split again, one to the computer for cable modem, and the other to my high def PVR. I have some audio dropouts and less often some digital pixelation on some high def channels, but I'm not sure if it's a signal quality problem or just a problem with the cable provider.