if you do not boil the wort, you will have a sour beer from all the bacteria and wild yeast that exist on the malted barley. Boiling the wort sterilizes it, killing off these normally unwanted organisms. Since you then add yeast, the beer is not pasteurized. Pasteurized beer would be when you kill off the yeast once fermentation is complete so that the end product does not contain any microorganisms.
The only beer style I know of that may not include boiling the wort is Berliner Weiss, a sour German wheat beer
Also...with no boiling, when/how will you add the hops?