There is the notion of Generalized RBF Kernels, for example in "Towards Optimal Bag-of-Features for Object Categorization and Semantic Video Retrieval" from Jiang (1) or in formula (2.72) in http://agbs.kyb.tuebingen.mpg.de/lwk/sections/section23.pdf (2).
They define: Gen. RBF Kernel: $e^{-pd(x,y)}$, where (1) says d can be any distance function and (2) requires it to be a metric.
I now have been wondering for a long time: Is a function defined by $e^{-pd(x,y)}$ where d is a metric always a Mercer's Kernel? I think in (2) it sounds like it, but if it were true, not many people know of it, since they are still looking to prove that $e^{-EMD(x,y)}$ is a kernel, where EMD = Earth Mover's Distance, which is a metric.
If its not a Mercer's Kernel - do you know of any counter example?