The Inflationary Big Bang is the most widely accepted theory for the formation of the Universe. This does not mean it is accepted universally! There are a number of scientists, of varying caliber, who do not feel the Big Bang has all the answers, and have proposed alternatives. Many of the alternatives have more issues than the Big Bang, so are not included here. I believe that, though there may well be corrections to it over time, the Big Bang cosmology is essentially correct. Critics have identified a number of issues with the theory, though most are explained by dark matter or inflation scenarios. Some criticisms are based on older data, like the age of the Universe being less than the age of some of the older globular clusters, where recent data have shown this not to be the case.
Most, but not all, of the cyclic universe alternatives do not stand up to scrutiny because of conflicts with the second law of thermodynamics. I have excluded these, for now.
A recent (July 2010) suggestion from Wun-Yi Shu of the National Tsing Hua University in Taiwan, proposes re-writing General Relativity and allowing the gravitational "constant" and the speed of light to vary over cosmological time. He suggests that, as the Universe evolves, time & space are interchangeable, with the (varying) speed of light as the conversion factor, and that mass & length are interchangeable, with the conversion factor as a function of the (varying) gravitational “constant” and the speed of light as: G/c2. There is an excellent refuatation by S.C. Kavassalis at Bad Physics.