most games also have an offline 'career' mode. Also some modern games have no multiplayer mode (such as Skyrim) but not being online means you miss out on 'additional content' (basically money-spinners for the developers.
I'm playing Far Cry 3 at the moment which is an awesome game in career mode but I'm told the multiplayer mode is weak.
Games like the Call of Duty franchise are more known for the online play. Its a case of sorting out the wheat from the chaff.
I can't think of one exclusively online Xbox game. As has been said above many do focus on the online experience and offer a poor single player game but there are still many decent single player games to be played.