Between 1999 and 2006 MMORPGs have gotten a lot faster in many aspects. Curiously that had little to do with advances in technology, but a lot to do with changes in perception about the value of time. As not everybodies perception changed, not all games have become faster. But a general trend towards faster games is definitely there.
On the largest scale, the time to level your character up to the highest level, World of Warcraft is probably the furthest away from Everquest. In Everquest, once the level cap had gone up to 60 with the Ruins of Kunark expansion, the average player took over 2,000 hours to reach level 60. In World of Warcraft the average time to level 60 is only 500 hours, four times faster than EQ. The optimum time to reach the level cap is a complex problem. If a game is too slow, the players level progress per session or per week becomes so slow that he has the impression to not progress at all any more, hence the description of "treadmill". If a game is too fast, lots of people reach the level cap and are at a loss what to do next. That arguably happened to World of Warcraft. The advantage of having a fast game is that you can raise the level cap, thereby making the time to hit the cap longer, until you hit an optimum value. World of Warcraft's Burning Crusade expansion will increase the time to level cap to about 700 hours, which is probably a better value than just 500 hours. But there will never be a consensus on the best value, because it highly depends on an individuals time spent playing per week, and that can vary anywhere between 10 and 100 hours.
Difference in time used for playing are even more noticeable on a smaller scale, the time it takes to perform some task. I remember in Everquest I was quad-kiting with my druid in a remote corner of Velious at level 42 (I never got any higher). It took me 5 minutes to kill the 4 snow leopards I was kiting, using up all my mana. Then it took me 15 (!!!) minutes of meditation to regenerate my mana back from empty to full. I had an alarm clock set, and was doing other things like reading a book during that time. In a group with an enchanter, this mana regeneration time between fights went down to 10 minutes, due to the enchanters Clarity buff. Fast forward to World of Warcraft where my level 60 priest regenerates from zero to full in 3 minutes when just standing around, and in less than a minute if sitting and drinking some water. Obviously the time between two fights has gone down considerably between Everquest and World of Warcraft. Other sources of downtime also got faster, for example waiting for a boat in Everquest could take up to 20 minutes, while in World of Warcraft the boats and zeppelins go every 5 minutes.
There are two reasons for a game to have downtime. The official defence of the Everquest developers was that during downtime people had time to chat with their group, thus downtime improved social cohesion and friendship. The more obvious but unadmitted reason is that by adding more downtime between fights and making your game slower, it took people longer to consume the content. So with less money spent on developers programming content your game lasted longer. Unfortunately that financial calculation didn't quite work out, because many people hated downtime and just left the game. World of Warcraft being shorter and faster just attracted a lot more customers, so even if the churn is higher, the financial results for the fast game are a lot better.
A third aspect of time is the smallest scale, the seconds or even fractions of seconds for a combat move. The principal problem here is ping, the time a signal takes to travel from your computer to the server and back, which is already in the order of 100 milliseconds for most people, but can go up to a second or more with lag. Thus MMORPG most often have some form of auto-attack, which continues even if the server doesn't get a signal from your computer. Or for spell casters a single signal starts an action that lasts several seconds of spellcasting. There is a trend to make MMORPGs more "action based", but due to lag that isn't quite as easy as making fast combat for a single-player game or a game played on a LAN. The combat in World of Warcraft isn't noticeably faster than the combat in Everquest. Games where some mouse movement swings your sword and actually hits whatever is standing in front of you, and not just the target you're locked on to, have been announced. But the viability of the concept has yet to be proved.