This is my build that I found the best for Singed. I played him for 8 months now with about 500 games so I took the time to analyze many aspect of game play with him. I put on my main build but you really need to adapt this to the game situation. It seems like the numbers on top don't add up to the real situation so I'll try to tell you the right ones below.

Health: around 4200
Mana: 3625
Health per sec: About 59 While not in ult
Mana per sec: About 14 While not in ult
Armore: 204
Dodge: 0
Mr: 189
Damage: 116
Crit: 0
AP: 210
Armore pen: 0
Magic Pen: 8,55 | 15%
Movement speed: 468

First of all, the runes. Movement speed is the key with singed. That's why my quints are all about it. This magic 4,5% bonus speed will make you go at 373 at the start of the game and, if eveything is going alright, 468 at the end. This movement speed is perfect to help you teammates with your fling.

Now, the marks are in magic pen for your poison and your fling to do max damage. Without them, you won't be able to hurt anyone badly.

For the seal and the glyphs, many choices are offered to you. Since singed is a bit low in magic resist at the start, I prefer putting most of the seal in this. And as for the glyphs, ap by level or flat AP is good. This should bring you to 39 Armore and 32 MR at the beginning and 204 Armore and 189 MR at the end. Which blocks at lot of damage...

The AP per level glyph gets you at 228 AP while the flat ap leads to 210 AP... small difference since you poison scale is low and fling scale is 1...

I go 10-5-15 in masteries to get the max usefull bonuses for singed.

The 10 AP bonus in ignite can be replace by 2 more armor points or some dodge chance but I don't advise it.

I'm getting the magic pen, again, to max out the poison damage and some AP per level in Offense.

For the defense, maxing MR and some Armor to get some tank attitude at the beggining is a must.

As for utility, I'm getting everything towards movement speed again. This maximize you chances of getting running ennemies or getting behind ennemy lines while initiating a fight.

This is where you gotta react to the game situation. The main build is: Boots of swiftness, Rod of ages and Force of nature.

Sunfire Cap can easily be replaced by thornmail if the other team as an auto-attack champ and the last rod of ages can be replaced by a banshee veil if they have a lot of Crowd controls.