This work presents CLTune, an auto-tuner for OpenCL kernels. It evaluates and tunes kernel performance of a generic, user-defined search space of possible parameter-value combinations. Example parameters include the OpenCL workgroup size, vector data-types, tile sizes, and loop unrolling factors. CLTune can be used in the following scenarios: 1) when there are too many tunable parameters to explore manually, 2) when performance portability across OpenCL devices is desired, or 3) when the optimal parameters change based on input argument values (e.g. matrix dimensions). The auto-tuner is generic, easy to use, open-source, and supports multiple search strategies including simulated annealing and particle swarm optimisation. CLTune is evaluated on two GPU case-studies inspired by the recent successes in deep learning: 2D convolution and matrix-multiplication (GEMM). For 2D convolution, we demonstrate the need for auto-tuning by optimizing for different filter sizes, achieving performance on-par or better than the state-of-the-art. For matrix-multiplication, we use CLTune to explore a parameter space of more than two-hundred thousand configurations, we show the need for device-specific tuning, and outperform the clBLAS library on NVIDIA, AMD and Intel GPUs.