The Bodleian manuscript
The 158 quatrains in the Bodleian manuscript have been translated a number of times. Very famous became Edward FitzGerald's translation (of a selection), and its subsequent revisions, based on a copy of the manuscript that he had received from E.B. Cowell. The discussion regarding FitzGerald's faithfulness to the original text resulted in a number of studies, initiated by an investigation by professor Zhukovsky, and carried on in the following years by other orientalists. One of these studies was done by Edward Heron-Allen, who published the Persian text from the Bodleian manuscript together with a literal translation in English. This study also included references to other sources with corresponding verses, such as the Calcutta, Bankipur, Lucknow and St. Petersburg manuscripts, and the translations by Nicolas and Whinfield, to mention only a few.
The references from Heron-Allen's study are now combined into a sortable table, including references from similar studies.
A number of translations are from a more recent date. Quatrains from those texts are not selected here, due to copyright restrictions. The quatrains presented here are selected from texts that, as far as I know, are now in the public domain.
The Omar Khayyam virtual exhibition, by the Bodleian Library, shows images from the original manuscript.