Any algorithms working with images need FPGA implementations to be quick enough, and there are a lot of convnets in use there.
There's a chapter on convnets here: http://www.cambridge.org/us/academic/subjects/computer-scien...
RNNs are nothing special in particular, at least these with small number of layers and nodes.
HMMs or CRFs are easier to handle for sequences, and would probably work well, and there are FPGAs all over the place of these models.