Here we go a few random brainstorm ideas:

1) Obviously a world, with night and day and weather patterns.
2) Distinctive classes and races, with each starting area being different.
3) An appealing art style- the old models were so very good.
4) Dungeons, so confusing and windy but great.
5) Items- people always longed for x and y items- everyone knew what a fbss was or a soy, and you knew where they dropped. And that discovery of getting armours with nifty clicky effects.
6) Danger- the trains, the giants, the griffins, the evily placed high levellers in low-level zones.
7) The Dragons.
8) Factions- you could be best friends with a city, or deadly enemies.
9) Grouping- now everyone knows whats what- but there was a time when everyone was still learning.
10) Discovering stuff. The quests weren't always straightforward and could be particuarly cryptic but you could sometimes find a solution to some obscure quest or whatever. (with a crappy reward though)
11) Roleplaying, Everquest could be THE perfect game for roleplayers. (this sort of went downhill with the perhaps watering down of its core fantasy environment)
12) Desirable advancements. You knew when the spell levels were(every 4/5 levels) and you looked forward to those sometimes quite distinctive spells.
13) Depth- you get encumbered carrying too much weight? oh okay. You need enduring breath to stay underwater? You need resists for this fight? Charisma is needed to keep mesmerizations lasting longer?
14) Other people- What would Everquest be without other people? to nab a mana regen buff or a sow of someone, to barter with someone, to setup mini, normal or large groups to take on certain areas, and negotiating with the strengths/weaknesses of the group.

I agree with almost every point there.

SOE weren't very good at making games imo - they weren't masters of user interface, balance, or even gameplay, but they did manage to conceive a believable fantasy world to lose yourself in.  Initially EQ was a very social game, where your relationships with people and your social status were just as important as how uber you were.

People became famous and almost celebrity-like by being knowledgeable about the game, and writing interesting posts on their class message boards.  Guilds were the ultimate social ladder, it was just a chat channel, but in some guilds (particularly the ones I was in) some people strived so hard to become officers, some of the biggest dramas I have ever seen in a game was when someone was insanely jealous that another person got promoted to officer.

People went crazy over things like who got their epic first, dozens of pages were written on guild forums about a new trial member.  Those recruitment threads were crazy.  It was like a nuclear war with words.

As EQ became more goal orientated - I think social interaction became secondary to the experience.  Oh sure, you still needed a guild to get anywhere, but people still cared a great deal about their reputations.

And it's this social aspect of the game that really isn't as prevalent in EQ anymore.  Perhaps it's because social players are more casual players and have moved on to other games.  Obviously WoW isn't anything like the communites we saw in EQ but it does have an energy about it; a buzzing excitement among players like it was back in early EQ.

EQ had the most entertaining guild dramas.  That's what I'll remember most about that game.  People seething, conspiring, betraying and crying over the personal issues that had nothing to do with the game really, just the people playing it.

15) TRAVEL - navigating a dangerous world could be more exciting than any combat...especially at the lower levels.  I remember making the run from Freeport to Qeynos as a lvl 16 wizard in order to purchase my copy of invisibility (because I was told that was the only place to buy it...ah to be a noob again).  It was my first experience running through Kith forrest at night (undead baddies all over), through Highhold (and the guardian orcs) and the Karanas.  Died twice in the Karanas, once to ghouls and once to a griffon, then a kindly shaman bestowed me with spirit of the wolf (first time I'd ever had it cast on me) and I finally made it to Qeynos.  I was completely lost in the game...immersed...for FOUR HOURS and many years and games later I still remember that run.  Luclin and Planes of Power pretty much ruined that aspect of the game.  BOAT !! 

I could come up with a few things like, it was the first, combat was simple to learn, complex to master (pulling, enchanters, timing of heals vs. aggro).

In the end though, it comes down to one thing and one thing only.

The Death Penalty.

That is it. That is what made the game great. Death HURT A LOT!

It made things extremely tense. It made you find a good team to do anything. Exploring was terrifying. In order to not die, you had to learn good tactics.

The death penalty made you think, and made you care about what you were doing.

Every game since, has had so little penalty for death that nothing seems interesting/tense/exciting. You might as well just read a website about the best place to hunt and then go do it and grind away. You die... who cares.