I have built him at times according to what is needed (team wise) and how things are turning out for our team (such as how teamfights are going) but personally I have fallen in love with my AD jarvan build, many bash it, but I find it many times very effective.
Philostone, HoG, merc treads are the 3 always grab items I go for, without a doubt no matter which build.
If I am going AD I will grab (afterwards)
Avarice blade, Brutalizer, Phage
Turn the AB and Brut into Youmuu
Zeal, Frozen Mallet, Phantom Dancer
my last 2 items I usually grab is Blood Thirster, and then black cleaver to finish it out
Gives me decent health, strong attack speed, strong armor pent, and 55% crit chance, I've had alot of decent games with this build, despite the fact I get bashed for building it. (if anyone has some better tweaks please let me know, I love testing out builds)
Tank Jarvan I go
Triforce, Merc Treads, Atmas, Warmogs, Banshees, GA (sometimes grab FoN, Randuins, Sunfire, and Aegis all pending on the other team)
Gives me a tanky build to take alot of abuse, allows me to initiate strong, deal out some dmg, and I can focus their high dmg output players
My question is what do most people find better in jarvan, a strong powerful AD champ, or a tanky jarvan who can eat some damage, and can still with his passive output damage.