Probability density functions (PDFs) of daily velocities from subsurface floats deployed in the North Atlantic and equatorial Atlantic Oceans are examined. In general, the PDFs are approximately Gaussian for small velocities, but with significant exponential tails for large velocities. Correspondingly, the kurtoses of the distributions are greater than three. Similar PDFs are found in both western and eastern regions, above and below 1000-m depth, with more significant non-Gaussianity in the North Atlantic than at the equator. Analogously, Lagrangian statistics in decaying two-dimensional turbulence also display non-Gaussian velocity PDFs with approximately exponential tails, in the limit of large Reynolds number.