Welcome to my Urgot build for a viable AP build.
To those of you who vote I'd appreciate comments so I have something to go off of why you think this is bad or good. To any who wish to say its terrible just from looking try it out before you say no.
Ghost: This is an all around usefull ability great for chasing people down or for running away. I don't play any character any more without it.
Flash: This ability I rarely use but with Urgot I find its beyond exceptional for putting you just in range of using your ult on someone.
If you find you don't like either of these options the only other viable abilities I could see would be one of the following.
Teleport: If for some reason your one of the people that can't seem to be able to stay in lanes for long and need quick way to get back.
Cleanse: Amazing ability even after it got nerfed. Removes CCs and reduces them for a few seconds after? I'd use if I didn't find ghost and flash needed for this champ.
Everything else is just a waste of your summoner abilities.
9/0/21 gives you best CDR, magic pen, maximized use of summoner abilities, and better mana regen and longer golem buffs.
Another build could be the 11/0/19 that I see a lot of people using. I don't care for as a couple armor penetration vs getting more use of your summoner abilities for ganking or surviving ganks is far better.
The first skill I max out is Acid Hunter, then I attempt to max out corrosive charge after I've got atleast 2 levels into your terror capacitor. I also max out my ult as soon as it becomes available to level up.
This is where a lot of people may or may not agree with me on my build.
I start by grabbing a Doran's Ring. I then save up till I can get a Rylai's.
Once you've got our Rylai's now all of your abilities slow with or without terror capacitor active. You don't have to be meleeing the person just acid hunter spamming them to chase them down. After this I generally grab my Merc Treads. For those who haven't really played Urgot much a good way to gank people once yo have rylai's is to come in drop corrosive charge on your enemy. Soon as thats applied immediately start spamming acid hunter. Save your terror capacitor untill you actually are being atacked back so that you have something to absorb a bit of damage. Before your rylai's if you use terror capacitor as you charge in and the above mentioned corrosive charge and then acid hunter spam you will get the same effect.
By now you should hopefully have your merc treads. If not obtain them imediately. Once you have your treads if your doing really well with gettinggold through kills and assists I would pass the guinsoo's rageblade and just aim for Gunblade. You should by now be picking up golem buff as often as you can so that you can nonstop spam skills and for the better CDR you get.
After your first gunblade it should be late game or starting soon. Your choices from here would be getting another gunblade, guinsoo's, or Zhonya's. I prefer to stack gunblades due the fact you get a lot of attack damage and ability power which all around beefs up all your skills(obviously not your ultimate). After you've got everything if the game has lasted this long I'd sell my doran's ring and get the Zhonya's if you didn't already. Instead of zhonya's or one of the gunblades you might find it usefull to get a lichbane which can be nice with your auto attacks. Otherthen this if you stick to staying in the back a bit and spamming acid hunter and keeping corrosive charge up as often as possible most people won't be able to get away. Obviously people with cleanse or some way of removing or becoming immune to slowing effect will but you'll do quite a bit of damage between your acid hunter and corrisive charge either way.
I hope ya'll enjoy my build and find it usefull. If you have any tips for me to add post a comment and I'll do my best to keep this updated and respond to comments.