We present an unbiased near-IR-selected AGN sample, covering 12.56 deg2 down to Ks~15.5, selected from the Two Micron All Sky Survey (2MASS). Our only selection effect is a moderate color cut (J-Ks>1.2) designed to reduce contamination from Galactic stars. We observed both pointlike and extended sources. Using the brute-force capabilities of the Two Degree Field multifiber spectrograph on the Anglo-Australian Telescope, we obtained spectra of 65% of the target list: an unbiased subsample of 1526 sources. Eighty percent of the 2MASS sources in our fields are galaxies, with a median redshift of 0.15. The remainder are K and M dwarf stars. We find tentative evidence that Seyfert 2 nuclei are more common in our IR-selected survey than in blue-selected galaxy surveys. We estimate that 5.1+/-0.7% of the galaxies have Seyfert 2 nuclei with Hα equivalent widths greater than 0.4 nm, measured over a spectroscopic aperture of radius ~2.5 kpc. Blue-selected galaxy samples only find Seyfert 2 nuclei meeting these criteria in ~1.5% of galaxies. We find that 1.2+/-0.3% of our sources are broadline (type 1) AGNs, giving a surface density of 1.0+/-0.3 deg2, down to Ks<15.0. This is the same surface density of type 1 AGNs as optical samples down to B<18.5. Our type 1 AGNs, however, mostly lie at low redshifts, and host galaxy light contamination would make ~50% of them hard to find in optical QSO samples. We conclude that the type 1 AGN population found in the near-IR is not dramatically different from that found in optical samples. There is no evidence for a large population of AGNs that could not be found at optical wavelengths, although we can only place very weak constraints on any population of dusty high-redshift QSOs. In contrast, the incidence of type 2 (narrow-line) AGNs in a near-IR-selected galaxy sample seems to be higher than in a blue-selected galaxy sample.