At the 2010 Games in Vancouver, no.
There is one sport that is for men only and that is ski jumping. The International Olympic Committee refused to schedule women's ski jumping at the 2010 Games. Their reasoning was that there was not enough interest and there are not enough countries with world class women ski jumpers. The IOC was taken to court over this in Canada but were not made to include women in ski jumping events as the presiding judge ruled that, while the exclusion of women was discriminatory, the Canadian courts have no control over the International Olympic Committee.
Look for women's ski jumping to be included in the events at the 2014 Winter Games in Sochi.
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Yes both men and women can compete in the Olympics in figure skating. The men and women are in two separate competitions- meaning they don't compete against each other, but at every Olympics there are male and female gold mentalists in figure skating. Also men and women can compete as a team in both Ice Dancing and Pairs competition.