In the 1996 Olympics, Ukraine earned 23 medals (9 gold medals, 2 silver medals, and 12 bronze medals). The gold medals:

2 gold medals went to 17-year-old Lilia Podkopayeva of Donetsk, the all-around champion and the floor exercise champion in women's gymnastics.
A gold medal to Rustam Sharipov in men's gymnastics, parallel bars.
A gold medal to Inessa Kravets in the women's triple jump.
A gold medal to Vyacheslav Oleynyk in Greco-Roman wrestling (up to 90 kg).
A gold medal to Timur Taimazov in weightlifting up to 108 kg.
A gold medal to Yevhin Braslavets and Ihor Matviyenko in yachting, in the men's 470 class.
A gold medal to Vladimir Klitchko in boxing, superheavyweight category (over 91 kg or 201 pounds).
A gold medal to Ekaterina Serebryanskaya in rhythmic gymnastics. In the finals she scored the highest score of all contestants in each of the four events: 9.950 in hoops, ball, and clubs, and 9.833 in ribbon. She had 3 of the 5 scores of 9.9 or better.
A bronze medal went to Ukrainian Yelena Vitrichenko for the all-round rhythmic gymnastics. (She went on to win the 1997 World Championships.)

Ukrainian medals in the "Games of the XXVIIth Olympiad":

Gold Medal in women's swimming: Yana Klochkova in the 400-meter individual medley - in world record time of 4:33.59, 1.20 seconds faster than the 1997 world record of China's Chen Yan. This was the first swimming event of the 2000 Olympics. Yana is 18 years old, 5 feet 11 inches tall, and weighs 152 pounds.
Gold Medal in women's swimming: Yana Klochkova won her second gold medal, this time in the women's 200-meter individual medley. She set a new Olympic record (but not a world record).
Gold Medal in shooting: Mykola Milchev in men's skeet shooting. Ukraine probably doesn't have an active Save the Skeet organization!
Silver Medal in men's gymnastics: The Ukrainian men's gymnastics team won the silver medal, finishing in second place behind China. Russia won the bronze medal, and Japan and the United States finished fourth and fifth, respectively. The members of the Ukrainian team were Valeriy Goncharov, Ruslan Myezyentsev, Oleksandr Svitlychnyy, Valeriy Pereshkura, Oleksandr Beresh, and Roman Zozulya.
Silver Medal in cycling in men's team pursuit, behind Germany. The members of the team were Oleksandr Symonenko, Sergiy Matveyev, Oleksandr Fedenko, and Sergiy Chernyavskyy.
Silver Medal in men's swimming: Denys Sylant'yev in the 200-meter butterfly.
Silver Medal in archery: women's team. Korea won the gold medal and Germany the bronze medal.
Silver Medal in women's swimming: Yana Klochkova in the women's 800-meter freestyle, her third medal.
Silver Medal in trampoline: Oxana Tsyhuleva in women's
Silver Medal in wrestling: Davyd Saldadze in men's graeco-roman wrestling, 97 kg.
Silver Medal in boxing: Andriy Kotelnyk in lightweight(60 kg) class.
Silver Medal in boxing: Sergey Dotsenko in welterweight(67 kg) class.
Silver Medal in wrestling: Yevgen Busloych in men's freestyle 58-kg class.
Bronze Medal in cycling: Iryna Vanovych in women's sprint.
Bronze Medal in gymnastics: Oleksandr Beresh in men's all-around.
Bronze Medal in judo: Ruslan Mashurenko in men's middleweight 90 kilogram.
Bronze Medal in synchronized diving: Ganna Sorokina and Olena Zhupina in women's synchronized 3m platform diving. individual trampoline.
Bronze Medal in track and field: Olena Hovorova in women's triple jump
Bronze Medal in boxing: Sergiy Danylchenko in bantamweight (54 kg) class.
Bronze Medal in sailing: women's team 470 fleet.
Bronze Medal in track and field: Roman Shurenko in men's long jump.
Bronze Medal in boxing: Volodymyr Sydorenko in flyweight (51 kg)class.
Bronze Medal in boxing: Andriy Fedchuk in the light heavyweight (81 kg) class.