If you are dealing with a pure protein where there is nothing else present that will absorb at 280nm and if the E(1%, 280) of the pure protein is known or may be calculated from the amino acid sequence, then A-280 measurement is a very accurate, fast, nondestructive method of determining protein concentration.
It is certainly much more reliable than any method that uses a standard curve, where the color produced may depend on the standard protein used.
It also has the additional advantage that the protein may be fully recovered after the measurement is made, often a consideration when dealing with precious samples.
It must be emphasized that the protein needs to be pure for this method to work. When dealing with impure protein samples, the 'rule of thumb' is that a 1mg/ml solution will have an A-280 of 1, or E(0.1%, 280) = 1. But of course other substances such as DNA or toluene (in a yeast extract, maybe) may absorb at 280nm and play havoc with your readings.
A-280 measurements, being nondestructive, are usually considered adequate for monitoring eluates from chromatographic columns.
If the amino acid sequence is known and you wish to use the Perkins (1986) method to calculate the E(1%, 280) it is probably worth bearing in mind that this method takes no account of a bound prosthetic group (such as haem or tightly bound NAD), which could also significantly contribute E(1%, 280) value.
Some good refs
Perkins, S. J. (1986). Protein volumes and hydration effects. The calculation of partial specific volumes, neutron scattering matchpoints and 280-nm absorption coefficients for proteins and glycoproteins from amino acid sequences. Eur. J. Biochem. 157, 169 - 180. [Pubmed] [pdf]
Gill, S. C. & von Hippel, P. H. (1989). Calculation of protein extinction coefficients from amino acid sequence data. Anal. Biochem. 182, 319 - 326. [published erratum appears in Anal. Biochem. (1990) 189, 283].
Sober, E. K. & Sober, H. A. (1970). Molar extinction coefficients and E (1%, 280) values for proteins at selected wavelengths of the ultraviolet and visible region. In Handbook of Biochemistry. Selected Data for Molecular Biology, 2nd edn. Sober, H. A., Ed. pp C-71 - C-98. The Chemical Rubber Company, Cleveland, Ohio.
Edit
I can give an example of the Perkins method, if anyone is interested.