Accepted for publication in The Astrophysical Journal (ApJ).We present observations of the J=1-0, 2-1, and 3-2 rotational transitions of N2H+ and N2D+ towards a sample of prototypical dark clouds. The data have been interpreted using non-local radiative transfer models.The authors acknowledge funding support under grants PNAYA2000-1784, ESP2001-4516, PNAYA2002-10113-E, ESP2002-01627, PNAYA2003-02785, PNAYA2004-0579 and the Madrid DGU PRICIT Program S-0505/ESP-0237 (ASTROCAM).Peer reviewed