Not everyone wants to group. If you play mostly alone, look for three things: something that tanks for you, a way to heal yourself and a way out when a pull goes wrong.
Pets: Hunter and Warlock
A pet that tanks is the biggest advantage a solo player can have. The 
Hunter gets in-combat traps for enemies that slip past the pet. The 
Warlock has Life Tap and Drain Life, so it rarely stops. Both sit at the top of our leveling tier list.
Self-healers: Druid, Paladin, Shaman
These three heal themselves between pulls, which saves a lot of eating time. A 
Druid can also run in Travel Form and stealth past enemies as a cat. A 
Paladin in plate is very hard to kill. A 
Shaman in mail with an hour-long imbue is close behind.
Harder alone
Rogues can skip fights with stealth but have no self-heal. 
Warriors are much better than before thanks to Victory Rush but still want a healer. 
Mages and 
Priests are fine alone once you learn to manage mana.
Elite quests and dungeons
Even solo players should try a dungeon or two. Forever has nine new five-player dungeons between levels 13 and 60, and tanks and healers find groups fastest.