The exact value of Eddington luminosity depends on the mass of the star and chemical composition of the gas layer. A rough estimate is 33000 solar luminosities per solar mass.
Gamma ray bursts, Novae and supernovae are examples of systems exceeding their Eddington luminosity by a large factor for very short times. In those cases, the result is a radical change in physical structure (namely, the ejection of a fraction of the star's mass).
Some X-ray binaries and Active galactic nuclei are able to maintain luminosities close to the Eddington limit for very long times.