Yes, some architectures (including x86) have instructions that hint to the branch predictor, but I think they still end up influencing branch predictor state.
There are four versions of a conditional branch: to be predicted, almost always taken, almost never taken, and too random to waste a predictor on. Compilers nowadays have "likely" and "unlikely" intrinsics, but offer, yet, none for the last. I think x86 now ignores its "likelihood" branch prefix because back when introduced it was too often wrong; and now compilers don't emit it because it they know it is ignored.
The "too random to predict" would be good for sorting, where it could provide a 2x speedup. To get the effect today you need to use conditional-move instructions, which have become unfashionable. Getting your compiler to emit a cmov is tricky.
Intel added a special instruction (maybe in skylake?) to use for spinning on an atomic flag update, that just halts until the cache line being watched gets clobbered by a message from some other cache. Compilers don't emit it, unfortunately, even when spinning on what they know is an atomic flag.
There are zillions of such instructions that were good ideas but were never taken up by programmers who they were meant for.
A prediction slot is where statistics on past behavior of a branch at a particular address accumulate. If no past behavior is needed to predict whether the branch will be taken, the predictor needs no statistics to decide, and statistics on some other branch instruction may accumulate in that slot instead.
If my understanding is correct, slots aren't really "taken up", but rather avoiding the branch predictor reduces the probability of hash collisions for other branches.
I also have a question for the crowd: for indirect branch target prediction, are the BTB slots actually tagged with the address? If you have BTB miss, do you pre-emptively stall the pipeline? It's more power-efficient to do so, but maybe it's better to avoid tags and tag-checking and spend that transistor budget on more BTB slots, and just go ahead and mispredict if you get a collision on BTB slots.