Generally speaking, a person who spends one of the nights of Chanukah away from home is not required to light Chanukah candles if his wife lights at home. He fulfills his obligation through his wife's lighting, and he therefore does not light Chanukah candles in his present location.
The Shulchan Aruch (677:3) does, however, make one exception to this rule (listen to audio for precise citation). Namely, if a person travels in a place with no Jews at all, such that he will not see any Chanukah candles that night, then he must, indeed, light Chanukah candles in his present location and recite the Berachot. This ruling is based on the position of the Mahari Abuhav (Spain-Israel, 1433-1493), which Rabbi Yosef Karo (author of the Shulchan Aruch) cites in his work Beit Yosef.
The Peri Chadash (Rabbi Chizkiya Da Silva, Italy, 1659-1698) disputes this ruling of the Shulchan Aruch, arguing that since the man fulfills his obligation through his wife's lighting, he cannot recite the Berachot over his own lighting. The first Beracha mentions that God "commanded us to kindle the Chanukah candle," and this individual cannot possibly speak of God as commanding him to light candles, given that his obligation is already fulfilled through his wife's lighting.
As for the final Halacha, Chacham Ovadia Yosef, in his work Chazon Ovadia (Laws of Chanukah, p. 158), follows the ruling of the Shulchan Aruch, requiring a person in this situation to light Chanukah candles with the Berachot. He adds that in such a case one should preferably have clear intention not to fulfill his obligation through his wife's lighting, so that according to all views he will now be required to personally light Chanukah candles and may thus recite the Berachot without concern.
This Halacha is very applicable to those who travel on business during Chanukah. For example, a person who travels during Chanukah in areas in the Far East with no Jewish community whatsoever must light candles with the Berachot even if his wife lights at home.
Summary: A person who is away from home on a night during Chanukah fulfills the candle lighting obligation through his wife's lighting. If, however, he is in an area without any Jews at all, he must light candles with the Berachot, and should preferably have clear intent not to fulfill his obligation through his wife's lighting.
