Introduction
Jarvan IV is a "DPS Tank" champion, and a very good one at that. I like to build him with HP, armor and some nice armor penetration/health-based damage items. Any items/order are situational, and can be changed according to the team comp you are facing or any other reasons you may have. This is my first build, and please feel free to leave constructive criticism after you try this build.
Past 6 games with him (Haven't tried him in ranked yet):

Changes
- 3/3/2011: Added Randuin's Omen instead of Frozen Heart. Also added Last Whisper if you have time to get it for the Armor Penetration. Added farming and jungling tips. Made some changes to introduction.
- 3/7/2011: Added Wriggle's for the WARDS, attack, minion farming, and life-steal; it's an all-around great item. Changed the item setup, found Heart of Gold (SOMETIMES 2) to be efficient for Jarvan and his item building as well as making him tanky enough to stay in fights enough to exterminate opponents. :)
- 5/27/2012 Totally revamped guide. Still working on changing intro and everything else, but this is a much more up-to-date guide.
- 9/13/2012 Another complete revamp. Been playing a lot of Jarvan (albeit not too high elo, 1650-1800), having some good success with him.
Pros / Cons of Jarvan IV
Pros:
- Good initiator
- Can be VERY tanky late game, while putting out acceptable damage
- Great at targeting squishy champs with his Ult; stellar in team fights
- E+Q can be used as a nice escape mechanism
- He has a Commando skin... Need I say more? :)
Cons:
- Not the most powerful DPS champ
- Ult can work against him if not properly utilized
Runes
I like to have the following runes:
Marks: Greater Mark of Desolation
Seals: Greater Seal of Resilience
Glyphs: Greater Glyph of Focus
Quintessences: Greater Quintessence of Desolation
Again, these may be changed for certain reasons, such as jungling, etc.
Masteries
I like to use a 21-1-8 build, as shown above. Sunder is important for Jarvan. I also like to put one in hardiness, just because :D. Since he lanes so well (E), I like to have Awareness as well, for the boosted experience. These can ALSO be changed, so be aware that this is not an END-ALL mastery list.
Skill Sequence
E and Q are important, especially E early game. This will allow you to gain armor and attack speed as well as harass with Q. The added bonus is you get to do your beautiful E+Q knockup combo, which is great for ganking and all-around harassment. (Useful for jungling, too)
W isn't that important, but I do like to have one point in pretty early for the added protection just in case!
Summoner Spells
I would choose Ghost and Exhaust/Cleanse. Depending on your opponents, you might need to take Cleanse over Exhaust for those nifty get-aways. I would pick Exhaust over Cleanse if you do not NEED Cleanse, though.
Ghost is just great for going into a fight AND getting out of it, so what's not to like?
Items
Now, there are many different combinations I use for Jarvan IV. Now, I do change this in-game according to what I need more / what I don't need, etc.
I have different items up for different situations:
Merc Treads: I'd use these obv for the speed and mainly the reduced CC. Can be replaced with Grieves or Boots of Swiftness if you don't need the reduction, or just want more attack speed or base speed.
Sunfire Cape: Awesome item for any Jarvan build I end up with. I almost never change this. You COULD use Force of Nature in place of this, I guess, but I would use Sunfire Cape AND FoN before I took out Sunfire Cape.
Randuin's Omen: Works great by slowing enemies, and works really good with your Golden Aegis. Also gives you VERY nice armor and health.
Black Cleaver: Great all-around, but AWESOME for the passive it has. Cuts right through the armor, and pairs perfectly with your Q.
Remember, anything here can be changed depending on the opposing team comp, etc.
Farming
When it comes to farming, Jarvan is very efficient. With his passive, it gives you great last-hitting with Creeps. E is also great for the attack speed AND armor, allowing you to clear Creep waves very quickly. Later on in the game if you're pushing for a TON of gold fast, or just pushing the lane (Split), E + Q is a KILLER for clearing waves.
I'd even put him mid/solo lane in some situations, due to his survivability and laning strength. You won't be disappointed with a good lane Jarvan!
Jungling
I haven't jungled with him too many times, but I like to start with Cloth Armor and 5 Health Potions.
From here, you can either go with your Golden Aegis OR your Demacian Standard. Personally, I go with E > Q > W.
I start at double golem camp, because Jarvan isn't the strongest jungler and I like to be safe when jungling with him. So I usually go Double Golem > Wraiths > Wolves > Blue Golem > Port Back > Double Golem > Red Lizard and then I get some ganks if I can.
Blue Buff can be pretty important to Jarvan IV, since it allows you to spam your E and Q (and W as well) much more often, keeping you alive longer doing damage in fights or harassing in lane.
Summary
This is a very good champ, and I have had a lot of fun with him. This is just my personal build that I wished to share with you guys; I am in no way saying this is the ONLY way to play him. This is just the method I have used in my previous games with Jarvan IV that seemed to work very nicely early - late game.