Vertical Resolution Patterns show you what the resolution capability of your system is
Vertical Resolution Pattern with Motion are similar but with the added element of motion, which can alter results
Horizontal Resolution Patterns - similar to above
Color Bar Patterns -- let you set the COLOR and TINT controls, among other things. here you get a version for the HD color standard and the SD color standard. You'll need colored filters at the very least, to use these.
IRE Window Patterns -- this are useful for setting grayscale, but require instrumentation for measuring the results and (usually) access to the service menu, to be useful. Also useful for gamma settings (again with instrumentation for measurement).
More color test patterns, again useful for calibration but require a measuring device.
IRE Full Field Patterns - again, for calibrating gray scale and gamma
More color tests.
IRE Bar Patterns - I find this useful for setting contrast (make sure the brightest area is distinct from the second brightest area) and brightness (ditto with the darkest two shades)
Ramp and IRE Bar Pattern -- similar idea, don't recall this one
Crosshatch with Circles Pattern - useful for checking convergence and geometry
Y/C Delay Patterns - can see y/c delay (like on the AVIA disc)
Overscan and Pixel Crop Pattern - can see how much overscan there is
A/V Sync Pattern -- makes sure sound and video match