I honestly don't know if these games are single player, multi-player or both. I do know my 11 yr old and 7 yr old grandsons James and Shane play them religiously. Those two are going to be major players in the gaming world as they get older! They play Plants versus Zombies and Minecraft a lot.
Another game they play quite a lot involves tunneling thru underground areas. They have their homebase in between encountering monsters. They also enjoy Spore in its various iterations. I hope these are single player, but I don't know since I don't play them.
Bottom line? Those two love gaming. James is probably nearly ready for WoW, at least to some degree.