The present (2003-04)
Today cosmologists try to determine not only k, Ωm, and ΩΛ, but also the age of the universe and the portions of Ωm due to various types of matter, such as baryonic matter, cold dark matter, and hot dark matter. They also would like an independent determination of the age of the Universe and the time that elapsed between the Big Bang and recombination, when atoms formed and the Universe became transparent. Amazingly, analysis of the anisotropies in the CMB, provides values for all of these and more.
Max Tegmark, et al (67 authors) attempt to determine all of the cosmological parameters based on analysis of results of WMAP, the Sloan Digital Sky Survey, and other data in a really, really difficult paper last revised in early 2004. If you can read this, you are far above Astronomy 350! There is a simplified summary on the SDSS website.
Note: There is nothing at all critical about the critical density if the cosmological constant is not zero, but the term is still used.
Cosmological Parameters:  1 2 3 4