This is (I think) actually the most op build for Singed ever done. Let's explain why.

Pros: -This champ deals tons of damages
-Singed can run wherever he wants
-Singed is tanky as hell
-News items of S3 made him godlike

Cons: -This build is maybe not tanky enough
-Can be highly kite..
-Hard time in early game

Why did I choose theses items ? It's simple.

-Rylai gives a annoying slow to your poison and to you fling, nobody will escape. It gives a good hp pool too with a little amount of AP.

-Seraph's embrace gives a lot of mana (so a lot of HP with Singed passive), gives a good shield to enter in a fight and gives a good amount of AP (It will help you while lane time, you won't get oom so easily with tear of gods).

-Liandry's torment is one of the best items for Singed now. The passive is just amazing, it will burn 5% HP of ennemies that you(ll touch with your Poison of Fling every 3-4 seconds! And here if the enemy is slowed, 10% of their life will burn (And it's here that Rylai help a lot!) ! This item provide some HP and some AP too, with 15 magic penetration.

-Rabandon is necessary to deal a lot of damages with your poison.

-Abyssal scepter will give you the magic penetration you were needing to get (and will give some AP more + Some Magic Resist).

This guide will make you being godlike on the battleground. Your poison+Liandry's passive will make enemies die rapidly. You may need to buy a tankier item (if you have to, remove abyssal scepter).

Have fun on League of Legends !

Syrach.