Lots of higher-end companies make bass cabinets with 12 inch speakers. Bergantino has already been mentioned, but they're also available from Aguilar, Eden, Schroeder, Epifani, Audiokinesis, and many others. More recently they've become available from more mainstream companies like GK. In addition you can absolutely use guitar 12s for bass if you really want to, though it may not sound that great. The problem you'll likely run into is power handling, since bass frequencies take much more power to reach the same perceived volume relative to guitar. Cutoff frequency will also likely be a problem. I really like the Eminence Private Jack for guitar, but it's only rated down to 70Hz. Looking at the response graph shows dropoff starting significantly higher; around 140-150Hz. The low-E of a standard-tuned 4 string bass is at 41Hz, putting the first harmonic at 82Hz. With this speaker the first harmonic will be audible, but attenuated by 3-5db (estimate based on the graph). Even a speaker with rather powerful bass like an EVM-12L (which I've heard Steve Harris used) is rather shrill and tinny when used for bass, or at least it was when I tried it.
PA12s are another option and tend to work rather well in my experience. The main caveat here is flatter frequency response as mentioned previously. However this usually isn't a problem as you typically don't want a colored cabinet for bass like you typically would for guitar. A potential issue here (maybe less so for guitar 12s) is XMax. Where XMax really matters for bass and where a lot of companies don't make the grade is farting out. If a speaker is in a box with incorrectly tuned ports and/or the wrong internal volume, it WILL FART OUT before you reach XMax.
I don't know about genres since you see it across so many, but tastes and amps certainly have. You still guys lugging around Ampeg SVTs & 810s, but the days when that was actually necessary are long gone. Thanks to advances in technology you can get a class D head that weighs 10 lbs and puts out 1000W at 4 ohms. Combine that with an efficient & properly ported cabinet or two and you end up with a rig that sounds just as good, just as loud (or louder) at less than half the weight. If you're really adventurous you can try something like
this. It may seem like a lot of hype, but I recently acquired a 12/6 cube and I've never heard anything like it.