EverQuest had its issues and Blizzard improved on most of them, but one thing EQ had that WoW doesn't is surnames. Once you hit level 20, you could choose a surname for your character. Star Wars:The Old Republic is implementing something similar, only you create a family name for all of your characters. I want to have Roblinator Shinycollector or Peenk Sparkles.
I would also love a sidekick or mentor system like in City of Heroes. Two players of vastly different levels can play together by temporarily kicking up the level of the sidekick or temporarily lowering the level of the higher-level character. I know we have Recruit-A-Friend and there are all those levels to be given, but it's just not the same as playing together in level-appropriate content with balanced experience gain. I want to invite friends to play and run dungeons together, not run them through dungeons.
Something I think we all would like to see is the level of character customization we find in so many other MMOs. I don't need to choose nose size or ear placement, but I would like to be able to choose a body type (like a healthier blood elf) and tattoos, scars, cosmetics, warts or whatever. For Forsaken body types, one of the choices could be to not have my bones sticking out of my clothes! Gosh, I want that so much. I'm OK with bones sticking out of my skin, but really, the clothes thing doesn't make much sense and is ugh-lee.
The thing that has always intrigued me about single-player roleplaying games and now SW:TOR is that there are often choices when doing quests and those choices affect your character. Yes, WoW has reputations that change how some NPCs react to us. But you can only select Accept or Cancel on a quest -- not really a choice. I wish I could take my character along her own path of neutral goodness and have that affect her options in the future, rather than having to torture things or sort through poop to progress through the story.
What surname would you choose? How would you like to customize your character? What are the features from other games that you would like to see in WoW?