In this paper, we develop a high-performance GPU kernel for one of the most popular dense linear algebra operations, the matrix-vector multiplication. The target hardware is the most recent Nvidia Tesla 20-series (Fermi architecture), which is designed from the ground up for scientific computing. We show that it is essentially a matter of fully utilizing the fine-grained parallelism of the many-core GPU in order to achieve high-performance for dense matrix-vector multiplication. We show that auto-tuning can be successfully employed to the GPU kernel so that it performs well for all matrix shapes and sizes.