To me, it all depends on the style of beer and the hops themselves, but overall, I like the hops. Most of my favorite beers have an IBU around 40 (+/- 10 or so). That would be like most American Pale Ales or mildly bitter IPA's. My favorite recipes that I have created include a big flavoring hop addition added at the last 20 minutes left in the boil using something that has a lot of citrus character like Amarillo, Cascade, or Falconer's Flight. So I guess that means I enjoy the hop flavor, but don't care much of the extreme bitterness. The aroma is great and I enjoy standing over the kettle taking in all the smell when I add hops, but I really want the flavor to come through more than anything in the final product.
Some of my other favorite beers included traditional hefes, saisons and other belgians, that have a prominent and unique yeast flavor, with low IBU, and low hop flavor. Some day soon I'll try making one of these styles with the same late addition of a citrus flavored hop. Just off the top of my head maybe something like 50-60% wheat, 2 row and munich, WLP380 for more spice and less banana, and lots of Amarillo and/or Falconer's Flight added in the last 20 minutes of boil. I'm imagining a mix of malty, spicy yeast, and citrus flavors that I think I would really enjoy.