Riven is a cooldown based Attack Damage Champion with no use for mana, energy, or Ability Power.
This is currently a work in progress, as this Champion is brand new. I'm working on a Cooldown reduction build to keep the mobility of Riven up and her enemies down.
This is not a Carry build, but meant to keep her as a fighter and take advantage of her mobility, stuns, regeneration, and shields.

Marks
Greater Mark of Desolation
Desolation Marks are the clear choice here, as all of Riven's damage is Physical. None of her abilities utilize and Ability Power, and white hits are necessary between abilities.

Seals


Glyphs
Greater Glyph of Focus
As stated before in the Introduction, this build is designed to get Riven's cooldowns as low as respectably possible, making these assist the overall design of her character.

Quintessences
Greater Quintessence of Desolation
The More Arp the better.

The skill sequence on this build may seem different, but I play hyper-aggressive.
With a good laning partner, or picking a champion with nice CCs, it's not too difficult to land a first blood starting with Ki Burst.
Ki Burst not only does AoE damage, but also a short stun, and procs her Passive for the next white hit.
Now that you can hit and harass, you need to be able to chase and escape.
Valor will help prevent you from needing to buy extra healing potions, and keep you in your lane longer, as the mobility from this, and the shield, will keep you moving and alive.
Once the basics are covered, it's time to put out some real damage.
Broken Wings is the staple that puts everything else together, and needs to be maxed first if you're playing offensively.
After Broken Wings is maxed, Valor should be next to start dropping incoming damage from mid-late game, and add to chases and escapes for teamfights.
Last but not least, maxing Ki Burst will help ensure you can lock down enemies for your team, and set yourself up to unleash a full Broken Wings combo.

For abilities, I use Exhaust to keep my enemies from getting away and lowering their resistances to ensure a kill, or to keep them from getting to me and my team.
Flash always makes a great emergency escape/dive mechanic.