Martin Foot's answer is a very good one. However there are a couple of things from my experience that I could add.
I've been told by some people that just a good rinsing will suffice and others say that your prints will continue (forever) to develop without it.
Yes, rinse with cold (running) water is enough. Cold water will stop the development process equally well like a stop bath. It will certainly not continue to develop forever. And it has other advantages:
- you can put a print back into the developer if you changed your mind. You'd kill the developer with a stop bath contaminated print.
- you wont contaminate the fixer with stop bath. This is usually not a big problem but if you want to keep the fixer for a long time it will
- you will not have the vinegar smell in your working room. (see below)
In my carreer I have seen a number of laboratoiries. There is actually only a single reason why there is a stop bath in the first place:
The lazyness of the casual photographer (see the answeranswer of aussiegeek)
Since photographers are usually lazy and don't care too much about cleanliness, the industry has invented the stop bath. It's something more they can sell and it makes the process more successfull for the average (lazy) photographer.
The first rule in your "photographic laboratory" should be: keep it clean. And "clean like in a kitchen" is not good enough. You should, whenever you think that your hands may have become contaminated with chemicals, walk over to the tap and wash! Do the same with all the equipment. Work as if all the chemicals are deadly poison - it is not - but that's the care you should take.
Don't underestimate the third point above. Your stop bath will be the item in your room that you smell even from the outside. If you work in this room for hours the smell can become mind-numbing. Some people are allergic to vinegar. Some photographers have become allergic to vinegar because of "overdoses" in the laboratory.
Care for your equipment is another point. You have your enlarger standing in the same room where your chemicals are. The vapors of the chemicals will have an effect on your equipment over the years. Not having a stop bath removes this cause.
What has been your experience? Will my prints disintegrate without Stop Bath?
No, the stop bath has no influence on the print quality. The quality of your fixer and how well the rinse after the fixer are essential for the quality of your prints.