In this paper we investigate how mass outflows from young stars relate to circumstellar disks by analyzing spectroscopic data of 42 T Tauri stars that span a broad range of infrared excesses. We measure the optical excess continuum (veiling) in each star from high-resolution 4 m spectra and extract forbidden line profiles uncontaminated by terrestrial night-sky emission, photospheric absorption lines, and telluric absorption lines.The veiling fluxes combined with existing infrared photometry allow us to estimate reddenings and stellar luminosities for the first time for heavily veiled stars. The new estimates of the stellar luminosities of these objects indicate that the stars with the highest accretion rates are the youngest in the sample. There is a one-to-one correspondence between forbidden line emission, veiling, and near-infrared color excess among the stars in our sample; all disks around young stars which are both optically thick and extend inward to within a few stellar radii of the stellar surface are, in fact, accretion disks, and have forbidden line emission. Residual forbidden line profiles of [O I] λ6300, [O I] λ5577, - [S II] λ6731, and [N II] λ6583 represent a range of critical densities from 104 to 108 cm-3. We have determined luminosities and line ratios for the two distinct velocity components in each of these forbidden lines. The high-velocity component resembles a dense stellar jet but requires more than a single shock to account for the observed line ratios. Luminosities of the high-velocity component indicate mass-loss rates of 10-8 to 10-10 Msun yr-1 for most stars and disk accretion rates derived from the veiling fluxes are 10-6 to 10-8 Msun yr-1. The mass outflow rates and mass accretion rates are correlated. The ratio of mass outflow rate to the mass accretion rate depends upon how the forbidden line luminosities are interpreted but is probably ∼0.01 for most classical T Tauri stars. The low-velocity component originates in a region of higher density than the high-velocity component and is characterized by a small negative radial velocity (∼-5 km s-1), possibly associated with a disk wind or magnetic accretion columns. The velocity shifts are largest for forbidden lines with the lowest critical density, suggesting that the low-velocity component accelerates away from the surface of the disk. If the low-velocity component arises on the surface of a disk in Keplerian rotation, then the observed profiles imply a disk surface brightness which decreases as ∼r-2.2.