This paper presents algorithms for parallelization of inference in hidden Markov models (HMMs). In particular, we propose parallel backward-forward type of filtering and smoothing algorithm as well as parallel Viterbi-type maximum-a-posteriori (MAP) algorithm. We define associative elements and operators to pose these inference problems as parallel-prefix-sum computations in sum-product and max-product algorithms and parallelize them using parallel-scan algorithms. The advantage of the proposed algorithms is that they are computationally efficient in HMM inference problems with long time horizons. We empirically compare the performance of the proposed methods to classical methods on a highly parallel graphical processing unit (GPU).