I have so many great memories of WoW that it's hard to know where to start, so rather than ramble on endlessly I'll just try to give an overall impression of why I love it so much.
One of my favourite aspects of any big game is the capacity for exploration. WoW is so rich, detailed and varied that it's a genuine pleasure to just... travel. Aside from the occasions where you change location dramatically (airships, teleportations, deaths, etc.) you never see a load screen. Each location blends seamlessly into the next, giving a solid feeling of a vast, living world. In my early days with the game I'd spend a great deal of time simply walking about, seeing where the road led. Oftentimes it led to a swift and painful death at the claws of something I had no right to be anywhere near, but on the flipside there's a sense of satisfaction from sneaking your way around a high-level area that's unmatched in terms of tension and excitement.
The realtime day/night cycle is essential to the immersion. I tend to play overnight, and I have particularly fond memories of one of my characters, questing solo through the small hours of the morning, occasionally glimpsing another night-owl player in the distance, and seeing the sun rise gradually ingame as it did outside my window. The ambient music and sound effects only add to the sense of place, and I can confidently say that no game has ever evoked such a feeling of being in another world entirely. The online aspect is of course a huge contributor to that - arriving in a town or city and seeing it teeming with activity.
I haven't even spoken of the gameplay itself yet. WoW tends to get a lot of unfair criticism for being little more than an online chatroom. I really don't see where this is coming from. It's among the most demanding, dynamic action games I've ever played. It's most emphatically not a simple case of standing in one spot and pressing attack. I never got too involved in the instances, but from what little I sampled I could see that there is a intense level of teamwork and strategic planning. Even on the overworld you have to be constantly aware of your position and surroundings.
Even the downtime stuff is fun. One of my favourite gaming things to do is to fish and cook in WoW. The relaxing nature of it is so appealing, and I'd often log in, wander to a lake or shore and simply fish for hours while chatting to other players.
On top of all this I have to mention that's it's a tremendously beautiful game. The artistic style is such that a lot can be wrung out of a very modestly-specced machine, and the use of colour in particular is excellent. Blizzard seem to have a gift for pinpointing exactly what appeals to the senses. It's a testament to the beauty and charm of the world that I sometimes renew my subscription just to wander around and see the sights again.