Scottish and Irish ales, English Brown ales, German lagers, lower OG or sweeter Porters and Stouts, hefeweizens, wits and many other Belgians, Northern German altbier and (to some extent) Dusseldorf alts, Koelsches, blond and cream ales, and all the hops alternatives (smoked malts and spice/herb/vegetable beers).
For the most part, just avoid the big, hoppy, "American" styles, and you are in pretty good shape.
I agree with Texlaw. There are a ton of styles you can brew effectively without making hop bombs. I've seen some great brewers do beers where there was only one small hop addition 15 minutes into the boil. Changing up when you add your hops will change utilization, which can have a huge affect on taste and aroma. The taste of your beers is as much determined by the malt profile as the hop profile. Also, I'm reading Brew Like a Monk, and there was a whole write up in the America section where brewers are talking about affecting the tastes of their beers by doing different things with the yeasts, fermentation temperatures, blending yeasts etc.
It's probably kind of hard to keep track of some of that stuff with the yeast in a non-lab environment, but it's worth exploring some of these things. 150 years ago brewmasters were working with far less scientific data than we do nowadays in a kitchen or backyard brewhouse.
I think not only what has been said above, but also using some less known or less comon varieties that will still be out there. I do not forsee having a complete loss of hops..just all of the most common and used hops. Some of the bittering hops will always be available..so think about these for your brews..
I meant as the sole hop addition. I went looking for a recipe on a couple of the blogs I read, and of course, now I can't find one. I'm going to take another look at Designing Great Beers later. I'm sure there were one or two in there.
Something tells me that we will be seeing a lot of "alternative" hop strains rising to the surface. Northern Brewer has recently started selling "Argentina Cascade" which is supposed to taste more like the noble hops than cascade. Hopefully this might broaden the way we brew.
Plenty of Belgian recipes emphasize malt, yeast and even candi sugar tones far more than hops. Hops are meant to be an accent in a majority of Belgians, not a primary flavor. If you have old hops with little left to offer in the way of aroma, use 'em in a pLambic. Lots of choices.