This is a deceptive question, because the questioner may want a short, or a long, time as the answer. So you have to ask back - why?
In Everquest, there are many possible paths through the lower levels before you reach max level, and all are rewarding. You can easily play a full account of characters on one server (8, up to 12 with purchases) without spending more than a little time in the same zones, until you hit the current expansion. Many people, possibly the majority of players, enjoy slow levelling - which can take as long as you want, especially if you choose to complete quests and gain high numbers of AAs along the way.
So this is for people who are in a hurry.
Based on what I have seen people post on TNZ, two days elapsed to hit 50. This would be following Crescent Reach -> Blightfire Moors as a path, no power levelling, with a tank merc, and is for any class. At the other extreme, under six months (closer to four months) for level 95 with 500 - 1,000 AAs, Void E access and a set of purchased gear from HoT. That would be enough to get you into most end-game raiding guilds, assuming that you are playing a class the guild wants. I'd guess that you'd need 4 hours plus per day play time, five days a week; but then you'd need that to join that sort of guild.
I have recently (February 2012) seen a report of levelling a cleric to 80 with 500 AAs in 11 days elapsed, with 5 days played; minimal grouping or power-levelling.