An artificial island built in the middle of the XIX century by the Tokugawas that turned into a futuristic residential area during the 80's. After the 90's crisis no many people was able to buy a house there, so it became a big commercial area. Includes the Fuji TV building (and its museum), several malls and a seafront with a small replica of the Statue of Liberty. It's connected to Tokyo by the Rainbow bridge and has the best views of the Tokyo skyline. Go by the Yurikamome automated train!
I lived on Odaiba for 3 months and can really recommend going there - the view from the small beach is great both day and nighttime, with lovely view of the Rainbow bridge and Tokyo skyline, as mentioned by chema.
There are many huge shopping departments on Odaiba, such as Decks, Aquacity and Venus Fort, as well as many entertainment complexes with bowling, karaoke and also Tokyo Joypolis. But beware - it's crowded with couples and families during the weekends.
I can also recommend to take the huge Ferris Wheel during nighttime - such lovely view! Going there by the Yurikamome line is quite fun even though it's a bit more expensive than most trains in Tokyo.