Putting meat on the bones
For my friend I picked the Alliance quest about the missing gryphon Sharpbeak in the Hinterlands as a starting point. I had already done the first part of it, but for the sake of roleplay I decided to pretend I hadn't. Everyone (except evil people) loves saving innocent animals, and my little gnomish warrior just loves doing heroic deeds for people, so it was easy to imagine her being very enthusiastic about it. My friend's gnomish warlock is much more evil and self-interested, but he saw some reward in getting paid for this service, and luckily a paladin friend of his around the same level just happened by, so the three of us set off together just bouncing off one another's personalities while we looked around the troll villages for signs of a gryphon.
Of course, having done this section before, I knew that the search leaves you coming back to the Gryphon Master empty-handed, but in the act of doing the quest, it was fun to stand in front of the quite obviously empty cages and say things like, "Do you see a gryphon in there somewhere?"
The paladin said, "You'd think there would at least be feathers or something."
My gnome replied, "Indeed you would! Perhaps there would also be wings. Legs. A body. Maybe even a beak!"
When you roleplay a quest, you can play off all sorts of ironies involved, such as in this case, it's kind of funny how you have to go and actually open these cages with nothing in them instead of just walking nearby and looking in. There are so many ways our characters can play off these things, even with just an incidental statement. Our creativity doesn't come so much in the content of the story, which is determined by the quest itself, but the individual way in which we take our characters through it. If you've even considered roleplaying at some point in your WoW career, you're probably not an entirely boring individual, and there's probably a lot of fun you can have by just responding creatively to the setting and theme that quests provide you with.
On the way back and forth between the Aerie Peak questgiver and the troll villages, we came upon the Mangy Silvermanes and Silvermane Wolves required for another quest in that area. It was a simple matter to just get that quest done at the same time, and even have a little bit of roleplaying fun while we were at it. When my warrior got attacked by a wolf, she would say things like, "Someone needs to train these dogs properly!... Sit!... Bad dog" --smack smack-- "Heel!... Bad dog!" --whack whack-- "Play dead!" --BONK-- "Good dog!" The warlock informed her that the wolf was not just playing dead, but my warrior cheerfully ignored the fact.
Quests like that which require you to just kill so many enemies or gather so many items are perfect as fill-ins to do along the way. You can think of all kinds of creative reasons why your character would be killing such monsters, of course, but it's more important that you do it with a bit of flair, cheerfulness, drama, intensity, or whatever kind of roleplaying you and your friends enjoy.
You can sometimes linger a little bit in each quest space, too -- often the time in between respawns is just enough for a character driven "story beat:" an interaction that engages your interest in the characters just enough to make you want to keep on going with them, but hopefully not so long that you end up spending the next 20 minutes or half an hour just sitting there talking. Of course you can certainly halt the questing process in order to sit and chat if you prefer, but one of the beauties of roleplaying through your quests together is that you really can gain experience and entertain each other at the same time.
Add a little color
Although at first glance, this may seem like a total-immersion form or roleplaying, I found that I enjoy it most when I can selectively choose which things I want to roleplay out as in-character realities, and which things I would rather just gloss over and discuss out of character. I really enjoyed talking about fighting the dogs, for instance, but it would have felt really weird to try and say things like "need to kill one more wolf" in character. It feels much more fluid to me to just say that out of character in party chat, then point to a wolf and say, "Look! That one reminds of my old pet Fluffy! Hello Fluffy!" and charge on over, thunk it dead, and say, "Well... it wasn't anything like Fluffy at all, actually. Let's go back now." This way my friends and I are all know what's going on at the level of the game's mechanics and quest requirements, but we're also enjoying the storytelling aspect as well.
In the end, that particular quest line fizzled out into a trip to Zul'Farrak that we didn't really have the time or energy for, so we had to leave our quest story uncompleted. While ideally we could have saved the cutsie widdle aminal, we all understand that we're not roleplaying together because the quest stories are all that fantastic. You can't rely on quests to start or finish in ways you would want them to, or even to always progress with a clear story logic you can understand. Sometimes it feels a lot like "okay, what do you want now?" every time you go back to a quest-giver for the next task you have to complete, and you just have to go with the flow as best you can. Even though some quests actually suit roleplayers perfectly, no matter what our quest-givers ask us to do, our real reason for being together is for that improvisational entertainment we enjoy and share with one another. The quests and other experiences within the game just provide a context for that, a kind of skeletal structure we can rearrange to some extent, in order to add the meat and skin we want our special creations to have. If you are flexible, sometimes you can make them work magic for you.
Indeed, my friend said that he actually enjoyed leveling for the first time in a long long time. The experience made me realize that for all the talk you hear of games like WoW being so unsuitable for roleplaying, there's actually a lot here that you can play with. The art of roleplaying in any medium essentially lies using your imagination to make the most of whatever tools you can share with your friends.