My current favorite ice cream flavor is VERY specific:
Rum Raisin from Tanner's Market. Tanner's is a local place that is a dairy-farm / grocery store. All of their dairy stuff is made right there on their farm and they are famous around her for their ice cream. My guy introduced me to their rum raisin and I never looked back.
Though I think Ben and Jerry's Chunky Monkey and Stephen Colbert's Americone Dream flavors are pretty good. They still aren't Tanners, though.
Out of the 3 classics, Strawberry is my favorite. But out of all of them, it would have to be Cold Caramel Fruitsalad. It's vanilla bean ice cream with caramel swirled into it, but with strawberries, bananas, & black cherries in it!