(covers information that was retroactively changed)
Rigel-class was the original intended starship class of the USS Zhukov, as it was listed in an okudagram in TNG: "Brothers", before the ship was seen in TNG: "Data's Day" as an Ambassador-class heavy cruiser. After the appearance of the ship, the okudagram was corrected. A later version of the graphic listed the Zhukov correctly as an Ambassador-class starship.
According to the Star Trek Encyclopedia, (3rd ed., pp. 4, 410, 513) the USS Akagi, mentioned, but not seen in TNG: "Redemption II" and DS9: "You Are Cordially Invited" and the USS Tolstoy, mentioned in TNG: "The Best of Both Worlds, Part II", were both Rigel-class starships. No specific model was ever built for the Rigel-class. The dialogue about the wreck of the Tolstoy being seen in the debris field in "The Best of Both Worlds, Part II" was added in post production to replace a line about the USS Chekov, a Springfield-class starship, that actually appeared on screen. Michael Okuda remembered,"Rigel: I don't think we ever came up with a ship design specifically tied to that name."  In the Star Trek Encyclopedia (3rd ed., p. 410), he also wrote that the designation Rigel-class was conjectural. Startrek.com incorrectly identifies the model that was labeled as USS Princeton as the Tolstoy in their Rigel-class article. 
According to the apocryphal Last Unicorn Games sourcebook The Price of Freedom, Rigel-class starships were heavy scouts, 215 meters in length, with a crew of 65. The ships had a maximum speed of warp factor 9.2.