L.A. Times obituary here. And since images are far more important than words, here is her first dance number in Nicholas Ray's Party Girl.
She was a great star who perhaps should have been an even greater star. Sometimes her filmography reminds me of a baseball player who languished in the minors for a long time before being given a chance to prove himself in the big leagues. Charisse was in "major league" productions at MGM almost from the beginning, but often in somewhat minor-league roles, there to do maybe one dance number and not much more. Actually, that's exactly the role she had in Singin' in the Rain, in the picture for one dance number. But most of her other numbers had been fairly wholesome, with some exceptions like her number with Ricardo Montalban in On an Island With You (see below). In this one, she was dangerously sexy and funny at the same time, funny because of the delight she took in disturbing and teasing Gene Kelly's hapless "Gotta Dance!" guy. And she wasn't even the first choice for that part; it was supposed to go to Kelly's longtime assistant Carol Haney, who was a marvelous dancer but wouldn't have projected the same kind of overwhelming sexuality.
One reason MGM didn't cast her in many good parts, apart from luck -- she was supposed to get the Ann Miller part in Easter Parade but got hurt and couldn't do it, and that set her career back some -- was probably her height; she was half an inch taller than Gene Kelly. (Comden and Green referenced this problem in The Band Wagon when Fred Astaire's character worries that she's too tall to be his dancing partner.) But they didn't seem to realize, until Singin', that her height could be an advantage. When Fred Astaire or Gene Kelly dances with her, they actually have to work to be her equals in the dance, because she's so imposing that she could easily take control of the whole relationship as expressed in dance. When she does overwhelm her partner, as she does when Kelly first sees her in Singin', it's funny because we're watching Kelly share our reaction to the sight of her; he's as overwhelmed as we are. And when Kelly grabs her hand and establishes himself as her equal, it's a great moment because he really had a challenge in being on the same level with someone who just a moment ago was in complete control of him.
It was Singin' that instantly made her leading-lady material at MGM, and got her the part for which she's best known, the part in The Band Wagon ... though the movie never gave her a really good solo number. ("New Sun in the Sky" is too short, and the cut "Two-Faced Woman" was part of Jeffrey Cordova's horrible pretentious Faust musical.) After that, she had two problems: one, that the musical was starting to collapse just as she had finally established herself as a star, and two, that there were very few parts in musicals that allowed her to demonstrate her distinctive sexiness for any real length of time. Most musical-comedy heroines are good girls, like the heroine of Brigadoon, a part that was perfectly suited to all the things Charisse didn't do best. Since she couldn't sing and wasn't a strong actor, a good Cyd Charisse part would have to lean mostly on her two outstanding, interconnected strengths: her dancing ability and her sex appeal. But musicals in the '50s were less dance-heavy than they had been, and heroines weren't usually written sexy.
Her best part in a musical after Band Wagon was probably Silk Stockings: Ninotchka's transformation into a sensual woman of the world allowed sex and sexuality to occupy a prominent place in most of her numbers, and Fred Astaire, despite his age, was a great partner for her because his dance numbers are very much about male-female sexual relationships. (Gene Kelly had more sex appeal than Fred Astaire, but his dances didn't lean as heavily on courship rituals and relationships, and they usually emphasized him a little more than his female partner, whoever she might be.) And of course her "Baby You Knock Me Out" number in It's Always Fair Weather is outstanding, though it's over too soon and she gets hardly anything else to do in the rest of the picture.
But it would have been interesting to see what she would have done with a part in a musical written for her specific strengths. MGM was considering a musical version of Anna Christie in the '50s; I don't know if she was ever considered for that (it eventually became the Broadway musical New Girl in Town with Gewn Verdon), but that's the sort of part I could see Charisse excelling in: a strong , sexy-yet-vulnerable role with lots of opportunities for expression in dance.
But never mind the stuff she could have done; I only emphasize that because I know others will be writing eloquently about the amazing work she did give us. One of the truly great performers in the history of film musicals.
On a tangent: I've said this before, but I increasingly think that in movie musicals, the most memorable performers are not the ones who are good at everything, but the ones who are weak in some areas and outstandingly strong in others. A movie musicals is judged on four things: singing, dancing, acting, and looks/sex appeal. Remember the scout who wrote about Fred Astaire: "Can't act, can't sing, balding, can dance a little" -- he was judging him on those four criteria. Some performers can sing, dance, act and look good (and looking good on film is a skill, one that requires practice and training just like singing or acting), but they rarely become legendary. Others, like Cyd Charisse, can't sing and have limitations as actors. But her strengths were so outstanding that she is a far greater movie-musical performer than other, more versatile perfomers. Sort of the way a baseball player with 40 homers and 100 walks but a low batting average and so-so defense is preferable to a player who can do everything fairly well but not outstandingly, a Cyd Charisse is preferable to a quadruple-threat performer who doesn't really stand out in anything. There, I've ended with a baseball analogy just the way I started.