Recently I came across an article on buying dictionaries and Ruth Wajnryb has just addressed the topic in her latest column. She comments:

Ergo, you need more than one resource. Linguist David Crystal boasts that he refers to more than 100 dictionaries. That’s perhaps a touch OCD but at the other end, one is too few.

Wajnryb compared three dictionaries and found that each had a different thought to contribute in order to attain a fuller meaning. The answer to the question of how many dictionaries, seems to be more than one but less than 100, no doubt depending on context and circumstance.