Alright, so you just got your super-cool Warhorse, you've probably picked up a few pieces of plate armor, and you're feeling invincible. What do you do? Well, unless reaching 40 was some kind of personal goal at the end of a long journey, you keep leveling!
Levels 40-41: Stranglethorn Vale. There are tons of quests here, some of which you probably already did back in the late 30s. If you're Alliance, grab the new Flight Path at the Rebel Camp in the northernmost part of STV. If you're Horde, pick up all the available quests at Grom'gol. Players of both sides should pick up any quests you haven't done yet at Nessingwary's Expedition (northern STV , along the river). You should also make the run down to Booty Bay in the south-- there are a lot of quests down there, some of which require trips back up north. There are lots of quest chains in STV , so if you have any green quests here, you should finish them up and see if there is a follow up (especially for the "Mastery" quests from Nessingwary's). If you're finding STV too difficult, consider Arathi Highlands (some of the later quests are around level 40-ish) or Desolace.
Levels 42-43: At level 42 you pick up new ranks of Blessing of Might, Flash of Light, Seal of Righteousness and Seal of the Crusader. You also get Cleanse, which should replace Purify when you're trying to get rid of debuffs. Like Purify, Cleanse removes 1 poison and 1 disease debuff, but it can also remove 1 magic debuff. It also costs the same amount of mana to cast, so there's no real reason to ever use Purify again.
On the leveling front, continue running quests in STV. If you find yourself running low on quests or just want a chance in scenery, you can take a trip to the Swamp of Sorrows, which is east of Duskwood and Deadwind Pass. If you're Horde, stop in Stonard and get the flight path, and stock up on quests. There's less to do here if you're Alliance, but there are a few quests to be found in the swamp.
Levels 44-45: When you go to train at 44, you'll pick up new ranks of Blessing of Wisdom, Exorcism, and Frost Resistance Aura, as well as a new skill -- Hammer of Wrath. Hammer of Wrath is similar to Execute for warriors (it can only be used when your target has less than 20% health), but since it is a ranged attack that causes holy damage, it can be used to finish off runners. And that's a good thing, because you should be questing in Tanaris now, where there are many mobs who like to run when they get low on health.
If you're Horde and looking to get to Tanaris, fly to Thousand Needles, then head east to the Shimmering Flats. In the southern part of Shimmering Flats, there is a road that goes through the mountains that leads to Tanaris. If you're Alliance, this trip is a bit of a pain -- take the boat to Theramore, then follow the road north until you find the west exit to The Barrens. Once in the Barrens, head south until you get to the Great Lift, which will take you down into Thousand Needles. From there, follow the Horde directions until you get to Tanaris. Almost immediately you'll see the goblin town of Gadgetzan -- the Alliance flight path is on the south side of the city, and the Horde flight path is on the north side.
There are lots of quests for both factions in Tanaris -- check all parts of Gadgetzan, as well as Steamwheedle Port to the east. If you like to grind (especially if you're Prot spec), then you will likely find Lost Rigger Cove (south of Steamwheedle) a paradise. It's filled to the brim with pirates that'll respawn faster than you can kill them.
Levels 46-47: New ranks of Holy Light and Retribution Aura, as well as a new blessing called Blessing of Sacrifice. This is a "tactical" type of blessing, because it only lasts 30 seconds (with a 30 second cooldown); however, it can be used to great effect in groups, and especially in battlegrounds. If you cast this on someone that is taking damage, it will transfer part of that damage to you, preventing you from being crowd controlled (remember, skills like Polymorph and Sap break on any kind of damage). I never used it much while soloing, though.
You've got a couple choices of places to level, here. You'll be coming back to Tanaris, so don't feel you have to clear out every single quest. No matter what your faction is, check out the Hinterlands (northeast of Hillsbrad, just north of the ruins of Durnholde). The Alliance town of Aerie Peak is just to your north as you enter, but the Troll run village of Revantusk is a little harder to get to -- if you follow the road that starts about mid-zone to the southeast, you should eventually see a path down to the coast. Once there, head south the Revantusk village (the flight path is out on the dock). There are quests here for both factions, but there are far more for the Horde, some of which have great quest rewards, so I wouldn't skip this place.
Alternatively, check out Feralas -- Feathermoon Stronghold in the west if you're Alliance, and Camp Mojache towards the east side of the zone if you're Horde.
Levels 48-49: You can train a new rank of Fire Resistance Aura, Redemption, Seal of Justice, and Seal of Wisdom at 48. If you're specced Holy, you can also pick up a new rank of Holy Shock.
If you're Horde, you'll likely still be working on Hinterlands quests, but if you're Alliance I like to head to Searing Gorge around this level (don't worry Horde players, there will still be lots here for you to do when you finish Hinterlands). The safest way for both factions to get to Searing Gorge is through the west exit from the Badlands. You'll emerge in the southeast part of the zone, but the flight path (and a good chunk of the quests) comes from Thorium Point in the northern part of the zone. There's plenty of quests here to keep both factions busy for a while.
Level 50: Whoo! I always breath a sigh of relief when I hit 50, because it generally starts to pick up again here (most of 41-50 is slow for me). This is really the last big milestone for your talent trees, because it means you now have access to the 41 point talents. If you're Retribution, you get Crusader Strike, which is an instant strike that causes 110% weapon damage and refreshes all judgments on the target. For Protection paladins, you'll get Avenger's Shield, which is a ranged ability that causes holy damage and dazes up to 3 targets. Holy paladins can pick up Divine Illumination, which reduces the cost of all spells by 50% for 15 seconds. All paladins get new ranks of Blessing of Light, Consecration, Devotion Aura, Divine Shield, Flash of Light, Lay on Hands, Seal of Light, and Seal of Righteousness. You also get a new spell called Holy Wrath, which is sort of an AoE exorcism -- it causes holy damage to all undead and demon targets within 20 yards of you.
I like doing the quests in the north part of Blasted Lands to get me going through level 50. They're all grinding quests, so you'll get good experience from kills as well as the quests, and the reward for each is a nice item that buffs one of your stats by 25. These quests are repeatable, but unfortunately the quest reward doesn't stack, so you can't farm up a bunch of them to help you level.
You're getting closer and closer to Outland, and it won't be long before you can get your epic land mount at 60 (which is well worth it, since it will likely be the fastest thing you can ride for a long time). Start saving money for it now if you haven't already, cause the increased mount speed is invaluable. You're almost there, so don't get discouraged! You'll make it, but there's a few more levels to get through first. Just keep swinging!