This is my suggestion of where to get experience, both in groups or soloing (hunting alone). If you are not certain where the zones I have listed are, go check out the links section and click on EQ Maps.
In my opinion it is best to go the Plane of Knowledge and ask (politely) if anyone can spare any buffs before you go and gain experience. The nicest buff to get is Temperance, a 800 health point buff, which also gives you a higher armour class. SoW (Spirit of Wolf) is a run speed buff, which is very useful to get about and to outrun monsters. You will gain faster experience if you group with fellow players, so if you are offered a group, take it. It is not always possible to get a group so check out the fear kiting guide for some good places to solo.
Hot Spots are zones where you gain bonus experience points if you hunt there, so they are worth checking out! These are the new hotspots released with the patch on February 28th 2008:
Level 20: North Ro and South Ro
Level 25: Solusek's Eye
Level 30: Blightfire Moors
Level 35: Stone Hive
Level 40: Dulak's Harbor
Do the tutorial and gain experience in the Gloomingdeep Mines. It is the safest and easiest way to gain experience, starter items and a small amount of cash by doing the quests and looting staffs from the gnoll spiritweavers (sell to vendors for 4pp each). It also shows you how to use the interface if you are new to Everquest.
11-15 I would suggest Kurn's Tower, for the best experience (XP) which is off the Field of Bone. You should be able to solo, but a healthpoint (HP) buff would be advised. Another place I like is the far end of East Commonlands at 11/12 and West Commonlands as you get a little higher. In both places you can either solo, or should be able to find a group. Clan Crushbone off Greater Faydark is also a popular place for grouping. If you wish to solo from 16 -20, get your panic animal spell at 16 and head to the Southern Karana's. There you can use panic animal to fearkite elephants (level 14-18) . Another option is Western Commonlands, where you can fear the kodiaks as they are level 14-16. Crescent Reach has some great newbie quests, so head over there for a change of scenery. A rule of thumb when hunting alone, would be to stick to animals that are the same or slightly lower than your level if you cannot get a HP buff. If you get a HP buff, then you can go slightly higher than your level. As you get nearer to 20, head towards Nedaria's Landing. For grouping at 16-20 then head to Paludal Caverns for the nicest XP.
Unrest is the current hotzone for this level - the experience is great! For soloing, Nedaria's Landing is the place to be for fearkiting, all the way until your early 30's. See the Panic Animal Guide for levels. If you wish to group, Paludal Caverns still has decent XP until 25. After this head to Solusek's Eye (Sol A) or Marus Seru.
30-40 I would recommend Stonebrunt for soloing and fearkiting (various animals - see guide). Another zone you can go to is Dawnshroud Peaks and fear zelniaks, although the XP and loot are not as good. Late 30's you may also try Eastern Wastes, but grab a HP buff. For grouping, Solusek's Eye is still good for a while and Dawnshroud Peaks always seems a busy place for grouping. The Great Divide and The Overthere, may also have grouping opportunities.