Probably the best MMO to start with if you are new to the genre.
Back when I started, it was early 2005, so PC game graphics weren't anywhere near as good as they are now. I have to say I was blown away by the beauty of the game world... not the technical complexity of the graphics, but the level of detail that the game designers put into the artwork for Azeroth. WoW is an extremely colorful game and everything in the game world feels like it belongs. Each zone on the map has a specific flavour - from forests to deserts to mountains to waterways. This IMO is the best aspect of the game - if you haven't played an MMO before I think you will love spending hours and hours just roaming through the wilderness exploring all the different things to see. The capital cities are also pretty amazing the first time you see them. Sure, the graphics are a bit over-the-top and cartoony, but it adds to the fun.
As for the actual gameplay, it is simple, but surprisingly addictive. Whichever class you play, you start out with only a few spells or moves, but by the time you have moved up to level 60 you will have about 30-40 abilities. And that is one of the things which keeps you playing - there is always something new which you can look forward to aquiring - whether it is your next level, a new ability, a new piece of equipment, a new recipe for one of your proffessions, etc. Blizzard obviously spent a fair bit of time adjusting the difficulty level of the game so that is just right. Combat starts out pretty easy, but then scales up in difficulty as you progress. It is easy enough that you can get satisfaction out of killing the various monsters and bad guys, but difficult enough that you can get quite frustrated if your character dies. I started out playing a warrior, and I used this as my main character up till level 60. I must admit I did get a little sick of using mainly the same moves over and over by the time I had reached the higher levels. I played a few alt characters with a different class - in hindsight I wish I had've chosen maybe a priest or a warlock rather than a warrior, but by the time I had levelled my warrior I had seen most of the game world so I couldn't be bothered going through it all again. There are good and bad aspects to playing every class, and they are reasonably balanced so that no one class has superiority over all the others.
Travel... As I mentioned, exploring the game world is one of the best things about WoW. Not just on foot either - at level 40 you can buy a mount (horses for humans, rams for dwarves, etc.). Mounts make travel much faster and when you first get one it feels like a real sense of achievement. (The expansion also has flying mounts for higher players). Travel between major towns or outposts is also possible by gryphon or bats, which is pretty cheap. When you take your first gryphon trip you will probably be amazed at the graphics and scenery (although maybe it is not so impressive now as it was in 2004 when the game first came out). But after a while these trips can become a bit annoying because to get from one end of a continent to another takes a fair bit of time, even if you fly. You will probably use the time for a food or toilet break.
I played on a PvE server most of the time, and this was fine for me. If you like being a bit more competitive though, you will probably like PvP servers. In PvP areas there is a bit more of an adrenaline rush because you never know when you are going to run into some players from the other faction. It can also be a bit more frustrating though if you get killed a lot, or if you can't complete a quest or get somewhere because the other faction is outnumbering you or camping. The best part of the PvE is instances (high-level dungeons which have elite bad guys)... for me this is the part of the game which I enjoyed the most. Completing instances can take a lot of teamwork, and each class has a specific role to play. In instances there a lot of variety in the monsters which you fight, and there is often a bit of strategy required to beat them. If you are playing with a group of friends you will love it - especially being linked up using teamspeak. The downside to doing instances is trying to get a group together, which can be easy enough if you are playing with friends or are in a reasonably large guild. But if your friends are offline it can be annoying trying to spam the chat channels to find the classes you need to get started.
Endgame...
I also spent a bit of time on raids (super instances which require 25 or more players) after I got to level 60. If you can join a decent guild you can have even more fun doing raids than instances. The sense of achievement you get when your guild takes down a boss for the first time keeps you coming back. It is a bit disappointing though how you might have to do a raid quite a few times though before you get the pieces of loot you want. The other part to the endgame is PvP - I didn't spend as much time on this but I tried it a few times. The battlegrounds can be quite fun if you want a distraction from the usual PvE levelling up or questing. It depends how organised you are - if you are in a team with friends or guildmates it can be great, but if you join a random battelground group then people are less co-ordinated so a lot of the time everyone just goes ape. Which can work sometimes, but it does help to have a team plan. Overall I liked battlegrounds, but if you really like competitive multiplayer games then I'd say go and play Unreal Tournament, Battlefield 2, or Guild Wars
Professions... The 2 crafts you can learn are another thing to do if you want a change from the usual gameplay. I found it was a bit tedious collecting all the ingredients, and even when you do, the items you can make are usually not as good as the loot which drops from monsters anyhow... But you can sometimes make a bit of money out of the collection proffessions (mining, herb-gathering, etc.) if you are dedicated enough. The in game auction house is also cool if you want to get into the economic side of the game or you are looking for a specific item or piece of equipment. And believe me, there is so many different items in this game that you would never be able to see them all. Sure, a lot of them are junk, but at the higher levels there are a lot of uber-items to eqiup yourself with which can make other players jealous if you get them.
Sound & music.... the sound in this game is pretty decent and well done as you would expect from a Blizzard game. I think the music is really great, and it is not too repetitive and really fits the game world. If you hear the music later on it will bring back memories of what you did in the game.
In summary, the best parts of the game are:
1. exploring the game world
2. playing with other players..
Sure, you can solo the whole game from level 1 to 60, but you won't have anywhere near as much fun if you do. The multiplayer aspect is what really drew me in. I made quite a few friends in the game, and also got a small group of real-life friends to sign up and play with me. Some days I just logged on to chat to friends for an hour or 2. The only problem playing with friends is if your friend spends more time playing than you do they will probably level up quicker. This becomes a problem if you want to do the same instances or quests together. One of the things that isn't good about WoW is that there a quite a few younger players who can be idiots at times... eg - spamming chat channels, and the Chuck Norris jokes soon get old. But like any multiplayer game there is a share of idiots, as well as some nice people you will run into.
WoW is a great MMO to play if you are looking for a fantasy game. If you can afford to pay the 15 bucks a month then I would get either this game or Lord of the Rings online. I didn't think $15/month would be worth it at first, but I ended up spending more time than I expected playing it, and I didn't spend much money buying other games for the next 2 years because WoW kept me pretty occupied. If you get WoW, I wouldn't bother getting the Burning Crusade yet unless you want to start as a blood-elf or a Dranei or a jewelcrafter... the original game kept me occupied for hundreds of hours!! I quit just before BC - not because I think it would be a bad expansion, but because after 2 years of playing the same game even WoW's gameplay becomes boring. You can always download the update later on anyhow.
If you can't afford a monthly fee then maybe try out Guild Wars. The graphics in World of Warcraft are now a bit dated, so if it worries you perhaps you might want to wait till Age of Conan comes out. On the other hand if you want something sci-fi or a bit more innovative, then give Tabula Rasa or Eve online a try.