Analysis of functional magnetic resonance imaging (fMRI) data is becoming ever more computationally demanding as temporal and spatial resolutions improve, and large, publicly available data sets proliferate. Moreover, methodological improvements in the neuroimaging pipeline, such as non-linear spatial normalization, non-parametric permutation tests and Bayesian Markov Chain Monte Carlo approaches, can dramatically increase the computational burden. Despite these challenges, there do not yet exist any fMRI software packages which leverage inexpensive and powerful graphics processing units (GPUs) to perform these analyses. Here, we therefore present BROCCOLI, a free software package written in OpenCL (Open Computing Language) that can be used for parallel analysis of fMRI data on a large variety of hardware configurations. BROCCOLI has, for example, been tested with an Intel CPU, an Nvidia GPU and an AMD GPU. These tests show that parallel processing of fMRI data can lead to significantly faster analysis pipelines. This speedup can be achieved on relatively standard hardware, but further, dramatic speed improvements require only a modest investment in GPU hardware. BROCCOLI (running on a GPU) can perform non-linear spatial normalization to a 1 mm3 brain template in 4-6 seconds, and run a second level permutation test with 10,000 permutations in about a minute. These non-parametric tests are generally more robust than their parametric counterparts, and can also enable more sophisticated analyses by estimating complicated null distributions. Additionally, BROCCOLI includes support for Bayesian first-level fMRI analysis using a Gibbs sampler. The new software is freely available under GNU GPL3 and can be downloaded from github (https://github.com/wanderine/BROCCOLI/).