Although there are lots of replies, I'm still going to throw my own into the mix.
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Why was FFXI 'so good'?
Content
I'm not going to lie. There were plenty of MMO's before FFXI, and successful ones at that. But what really pulled people into this one in particular? ... The Final Fantasy franchise. With so many games, and such a huge history, FFXI pulled many people into what would be their 'first' MMO. What makes a FF MMO different from other lore-based MMO's is the fact that Final Fantasy always has certain elements (such as chocobos, elements, avatars), but will not explore the same world twice (unless you are playing a sequel, and X-2 was not released until after XI came out). Therefore, you could play each new FF and 'fall in love with it' all over again, just as many people 'fell in love' with FFXI.
People often complain about the time sink compared with other MMO's. Yes, FFXI took SO MUCH TIME to level... but those 'grizzled veterans' coming to the MMO world from the Final Fantasy franchise were used to this. It took a long time to 'grind' your way up to get the best items and weapons in previous games... not a long time compared to the years you could easily log in an MMO, but FF players were a bit more tolerant of this type of time sink than others.
Timing
FFXI came out when MMO's were really starting to improve. There was always the iconic Everquest, but WoW would not come out for quite some time after the NA release of FFXI. By the time WoW did come out, so many people were already hooked on FFXI and absorbed into its world that they did not even bother with WoW, and if they did, they would usually come back disappointed. This is why you might notice a particularly large amount of hostility toward WoW in general with FFXI and FFXIV. Many FFXI and FFXIV player will bash WoW because it's 'so easy' (and it is in comparison), but the real reason you'll find it in this community over others is because the two were released at about the same time, and were each other's 'competition'.
Community
The time sink of FFXI really gave it this extra element of community that you would be hard pressed to find in other MMO's. There were NM's you would literally have to wait days for. Even the 'common' NM's would not pop for at least two hours, and there was no guarantee that it would pop or drop for you. Daily NM's could pop between 21-24 hours after they died, and only in 30 minute intervals between the start of the window and end of the window. Some NM's wouldn't pop for weeks. This left a lot of time to chat. You really got to 'know' your community. The theft of an item, or the betrayal of a friend, meant so much more in FFXI than any other MMO I've ever been a part of.
The time it took to level also allowed you to 'get to know' your party members. Because leveling wasn't easy for everyone, you got to know who was good and who was bad. The entire server 'knew' of each other. Some were famous while others were infamous. Applying to a linkshell required more than just skill -- it required attitude evaluation as well. When entering something like Dynamis (an instance that took 3+ hours to complete, IF you could complete it), you would want to make sure you liked the people you went with.
Identity
As a result of how hard it was to level, you really had to commit to your job. You had to spend weeks and weeks leveling it to 75, doing all of your job quests, and obtaining gear for it to be useful. Therefore, people got to KNOW you as that job. You weren't just your name. You were your name AND your job. I had three jobs at 75 -- Summoner, White Mage, and Black Mage. To this day, all of my FFXI friends know that my favorite job was and will always be summoner. In other games, it is easier to level. Having jobs at a cap level is not such a great accomplishment. Because the servers in FFXI were pretty small, you were more likely to recognize anyone you came across. Reputations developed... both good ones and bad ones. You knew who was likely to help out and who was a jerk.
Storylines
The 'story' of any FF game has always been SE's forte. The storylines took a long time to complete, and involved intricate lessons that you can really only appreciate if you did them. Each expansion was like a new FF in a familiar world. The content never left you 'high and dry'. There was literally ALWAYS something you could be doing.
Gear
One thing about FFXI that was very different from other MMO's is how your gear would remain at about the same quality no matter how long you took a break. The reason for this is because gear mattered a lot and so you would switch gear for each situation. Black Mages would switch to elemental staves depending on the spell, for instance. People would sometimes switch gear just to use a weapon skill. As a summoner, I would switch gear when using an avatar's ability. You switched gear a LOT, and so each piece of gear never became 'obsolete'; it was merely another option that you could be using. So, even if I took a break and came back years later, my gear was still great... And yet, despite this, there was always gear every person wanted to get and had to work to obtain. Very few people had everything they could possibly want.
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Why did Abyssea 'ruin' FFXI?
Level Cap
The level cap increase that came along with abyssea and other DLC brought about a huge flux in gameplay. After the NA release, the level cap was raised to 75 and left there for four expansions. Every single 'endgame' event was synced to this level cap, including content from all previous expansions. This is why content from the original expansion would be comparable to an expansion that came out many years later... because, unlike other MMO's, the level cap DID NOT change.
This change in level cap also more or less turned the gear you had spent years acquiring into garbage. All new gear was released, and somehow FFXI was thrown into the same category as other MMO's... with each level increase, or new content available, your previous gear became less and less likely to be used. To many players (such as myself) that could come back to the comforting thought that your gear would never be outdated, this ruined our desire to play the game. The FFXI we 'knew and loved' was torn apart by the level increase...
Not to mention, Abyssea itself more or less broke the game. The amount of experience points you received in Abyssea per time spent was staggering and unlike anything seen before. Obviously, they needed to do this to keep the game going (remember, it is older than WoW!), but more or less made it a different game. All endgame content was made easier so you could do it with less people (because there weren't as many people around). I, like many others, simply lost interest.
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In conclusion, I'll tell you what I see when I look back on FFXI. I see it with rose-tinted glasses and a nostalgic outlook. I will often sit around with my current FFXIV guild (all people I knew from FFXI...) and joke about how hard FFXI was, and all the ridiculous stories we have as a result. People would fall asleep waiting for monsters to pop, and somehow mysteriously not get mauled. Other fights were so hard (literally took days to master) that they were constantly imprinted in everyone's memory.