Files containing limb darkening coefficients can be downloaded from this page. The basic reference is
which contains information on the types of coefficients (monochromatic, bandpass-specific) and the format of the tables. The coefficients are based on the stellar atmosphere models of Robert Kurucz. I have computed coefficients for 19 chemical compositions ([M/H] from -5.0 to +1.0) and for 26 photometric bandpasses. The VH93 bandpass list has been extended and now includes the Hipparcos, Tycho B and V bands (response curves from Bessell, 2000, PASP 112, 961), six UV bands (rectangular response curves of width 20 nm and centered at 230, 250, 270, 290, 310 and 330 nm), and a 22 nm wide trapezoidal shaped bandpass centered at 858 nm near a CaII triplet. Coefficients for the latter non-standard bandpasses were computed at the request of Gene Milone. Clicking on a file name below loads the file in your browser. Bandpass-specific files are on average 800 kB in size, the unzipped monochromatic files are approximately 50 MB each. Abundances are indicated in the names of the files. A simple interpolation program written in FORTRAN can be downloaded by clicking here. Before using the program, read its comment lines carefully.
Note added July 7, 2011: I am in the process of calculating band-integrated limb darkening coefficients for many more bands including COROT, KEPLER, GAIA, and many others. This page will be updated soon.