Are all known germs benign in small enough quantities? i.e. Why do we wash our hands?
There is a Wikipedia page  which gives some typical values for infectious doses of bacteria. I suspect that lot of these have been taken from this slideshow which confirms the values on the Wikipedia page, gives more interesting details of how they have been arrived at, and also mentions a few viruses. 

It seems from the slideshow that infectious dose isn't estimated in the way that the OP envisages - "What is the probability of infection if I ingest one cell?".

What is clear is that the infectious doses for some bacteria can be less than 10 cells (e.g. Shigella flexneri, E. coli O157:H7). Conversely for many other pathogens such as other strains of E. coli the estimate is >106 cells, so standard hygiene precautions will always offer some protection.