The 6080 was designed as a low-ish voltage high current series regulator (essentially a high current triode with very low plate resistance) designed in the late 50's/early 60's. These are really tough little bottles that can burn of a ton of heat, and since you can boil a lot of current through them, they work pretty well run as cathode followers.
Since their inception, these have been used pretty frequently as output tubes in OTL amps, as their plate resistance is nice and low, and the tube cost is pretty low. Unfortunately, the matching between halves is fairly marginal (it wasn't important for the original design), so push-pull OTL can be kind of tough. On the other end of the spectrum, some people have made simple push-pull amps out of these, as a 2.5-5k output transformer is easy to get and perfectly reasonable as a load.
There are other similar tubes like the 6336, or the paralled double triode 6C33.