Been playing Zynga's CityVille recently. Some interesting points to note down for games with multiplayer elements, meaning games which allow you to play with or against other players.
1. People like competition. Competitive ladders like those which exist on Starcraft 2's Battle.net allow people to see how they rank compared to other players.
2. People like to show off. Allow people to show off their in-game achievements to others in the form of in-game rewards, eg. portraits in SC2, new buildings in CityVille.
3. People like to interact, socialize. Chat system, a messaging interface. Ways to organize and play in teams, eg. Chat channels in SC2's Battle.net, messaging/notification feature in Cafe World, CityVille, trade channel in World of Warcraft.
4. Reward system for achieving game-design goals and encouraging good social behaviour, eg. Zynga's RewardVille encourages players to play Zynga games to unlock in-game rewards.
5. Quest system which introduces game objectives/features and rewards the player for achieving these objectives.. This could take the form of an unfolding story eg. in Cafe World the player is encouraged to serve coffee and unlock more coffee recipes in order to view the story between Espresso Joe and Lisa Latte. Another way this could be done is to allow the player to unlock game features via completing quests. This ties into point 4 above.
That's all I can think of for now =)