In my handy-dandy Jungian book there are two full pages on the meaning of the number three. To say it is a magical number is the grossest of understatements. Where to begin? Well, it's nearing Easter so how about Father, Son and Holy Ghost?
Or, if that's too heavy for you, try three blind mice, three little pigs, three strikes and you're out, three men in a tub, three coins in a fountain, three on a match, etc.
Three is magical because everything from the beginning of time, was organized in threes. Think a minute. Morning, noon and night; sea, earth, and sky; animal, mineral, vegetable; past, present and future; beginning, middle and end.
In Hades there are three-headed dogs, Neptune has a trident, there are three Graces in mythology, and the three virtues of faith, hope and charity.
The lists above just scratch the three surface. What's really important to the dreamer is what the number three means to him or her. Dreams can always be looked at archetypically or classically but often, that isn't much help to the dreamer who keeps dreaming of threes. The real question therefore is: If you dream of the number three, what does it mean to you? Have fun with it, go with Gestalt, ask yourself if I WAS a three what would I be like? What number would I be attracted to? Like I said, have fun with it.