I'll do women's cross country à la CaroLIza_fan. On a much lower level though Help me if I got something wrong or forgot someone. Most is from my memory.
Norway Norway, Norway, Poland, some Swedes, Fins, Germans, Slovenians and Americans. I don't know much about the Russian women. They didn't compete last weekend(Feb 2-3) and none has been that successful this season. Japan seems to have only Ishida left as a completive skier, but she is hardly a medal contender.
Marit Bjørgen, at her fourth olympics (medaling in all former 3), will probably be in a class of her own. Queen of cross country in Vancouver(5 medals, three gold). Can do even better in Sochi. She will paticipate in five, maybe all 6 disciplines. Won the 10 km classic and free style sprint last weekend.
Women challenging her at long distance races are her team mate Johaug, Kowalzyk(POL), Kalla(SWE), maybe Saarinen/Niskanen(FIN) and Weng(NOR). Norway will win the 4 x 5 km relay. I think they could provide two teams, and both would be gold medal contenders Relay predictions: Norway(gold), Finland, US or Germany. No medal for Sweden this time. Russia?
Sprint (Free style), is a different matter. More contenders and unpredictable because of crashes, falls, tactics in a tight field etc. Denise Hermann(GER) is the leader of the sprint cup this season. Number two is my sentimental favorite, Kikkan Randall(US), also in her fourth olympics. If I remember correctly she fell at the semi final in Vancouver and I thought "poor her… four years until next chance". And here it is GO Kikkan! Others who can do well: Hanna Eriksson(SWE) Slovenia(Visnar, Fabjan), a Swiss and a Slovakish woman, Bjørgen and a couple more Norwegians, Kyllönen(FIN), Tjekalova (RUS) Probably not Kowalcyk, who is better at classic style.
The team sprint will be between Norway(if Bjørgen competes they will win), US, Finland, Sweden, Slovenia and maybe Russia….