My go-to is good old strawberry, including in a mild shake form, but I love berry flavors in general and will try just about anything that includes them. Fry's, over here in the southwestern United States, has a brand called Private Selection that features a number of pretentious, hoighty-toighty berry flavors, like a cherry with chocolate flakes, a vanilla and raspberry with cake pieces rolled in, and other indulgent nonsense that I shouldn't like but do. Yum yum.
I also enjoy Ben & Jerry's now and again because of their wonky flavors. I adore the red velvet cake flavor, although I have to be in the mood for it, and I'm patiently on the hunt for their pumpkin cheesecake flavor. It will be mine.
I'm not above more simple offerings - sometimes nothing will do but a soft serve vanilla cone - but the only flavor I really just don't care for is chocolate. The only thing I flat out hate in the realm of ice cream is nuts, though. There needs to be a circle of hell for the little hard, unwelcome invaders in my otherwise soft, delightful experience.