We provide the most precise measurement of the WW production cross section in p-pbar collisions to date at a center of mass energy of 1.96 TeV, and set limits on the associated trilinear gauge couplings. The WW->lvl'v (l,l'=e,mu) decay channels are analyzed in 1 fb^(-1) of data collected by the D0 detector at the Fermilab Tevatron Collider. The measured cross section is sigma(p-pbar -> WW) = 11.5 +/- 2.1 (stat + syst) +/- 0.7 (lumi) pb. One- and two-dimensional 95% C.L. limits on trilinear gauge couplings are provided.