Not Updated For Current Season
First of all, DON'T FLAME!
I never really played Urgot more than a bunch of times and I designed the whole build in 43 minutes.
The idea for this build is to have a tank/support/innitiator/DoT champion.
It's main purpose is NOT to have 20+ kills with only 2 ***its, it's just the opposite.
I chose 9/21/0 to keep up a nice tanking ability while making perfect use of Urgot's passive and maximize his safety when using hyper-kinetic position reverse.
As we'll be using AP as his main feature, we should max Noxian Corrosive Charge first.
This makes a nice DoT (damage over time) effect, helping your lane partner getting some kills.
I picked damage on level marks and quints for late game utility purposes, cdr glyphs for early game spamming and dodge seals for Nimbleness synergy.
The item purchases are simple: Doran's Ring or a Doran's Blade and a hp pot to increase your time in the lane.
Once you have the gold you should get your boots (always situational, but for this build Mercury's Treads rock. Banshee's Veil for HP and awesome passive (let's you use your ulti without being disabled by, for example, Enchanted Crystal Arrow). Hexdrinker is also acceptable.
After that you should invest in Sword of the Occult, so you aren't completely AD useless. I usually don't go for snowballing items, but as a tank/support (and if well played) I think it's really no problem. You can always pick Guinsoo's Rageblade or Manamune if you don't really want to go snowball.
From here, Rod of Ages is an awesome pick, as it gives you awesome AP, HP and Mana, as well as over time bonuses. You can also get Rylai's crystal scepter for (almost) the same features and slow (though, with the new patch, it will be a ****py one), or [[Abyssal Scepter for the magic resistance and aura, that I consider heavily underrated.
Nashor's Tooth can give you a slightly better DPS/farming ability, while reducing your cooldowns by 15% and granting you 55 AP. It's really an item that every DPS hybrid should get. If you don't feel tanky enough get Frozen Heart instead, especially if you got Manamune instead of Sword of the Occult.
After that you can go Zhonya's Ring, to have it's awesome active, passive and super AP, or be even more tank and get Guardian Angel, Randuin's Omen or a Sunfire Cape.
Short note on Hyper-Kinetic Position Reverse: I didn't gave him any armor at all, as he gets bonus while using it. It's use as a team fight innitiator (when it's 5vs5 anywhere and no one takes the first action) should be simple: R > veil first ability > zhonya's > cleanse > flash out.
Feedback would be much appreciated, thanks.