Flash is the best choice for a Riven, even if you think you have enough mobility.
Ghost is a good replacement for Flash.
I find this the best spell after flash for the epic damage over time.(True Damage)
If you don't like Ignite.
If you don't like Ignite or Exhaust.

Pros

- High Damage
- High Mobility
- Hard to gank
- Strong early and mid game
- AD boosts her skills
- Fun to play
- Multiple crowd control

Cons

- Needs good Timing
- Easy to counter with armor
- A focus, kills her really fast

Starting Items: Boots + 3x Health Potion or Doran's Blade.
Early Items: Try to get The Brutalizer after your first recall. Then get a Ruby Crystal and a Vampiric Scepter. If you do really good on your lane, rush a B. F. Sword. And then the Vampiric Scepter, Ruby Crystal.
Most used items I use on Riven: First item is Bloodthirster. The second item is Black Cleaver.
The third item is Maw of Malmortius. The fourth item is Randuin's Omen and the last item is or Another Bloodthirster or a Guardian Angel.
Of course your first item is your boots, you can get Ionian Boots of Lucidity or Mercury's Treads. If you fights against an heavy AD champ top get Ninja Tabi.

Now some item explanations: (The damage Items)
This item is your main damage item, it gives you massive AD and some life steal. Rush this as soon as possible if you think you can beat your opponent easily.
It also gives your E a really nice boost. So it's also effective for escaping a gank or team fight.

This item gives you some AD, some hp and some armor penetration, but the main reason you get this item is because you debuff your enemy (An armor debuff what stacks 4 times and reduces 25% armor when fully stacked.).

This item gives you some AD and mag res. The mag res is really nice if you play against heavy AP champs. The more AP champs the enemy has the more reason to build it. Also if you own your top enemy easily and the enemy has a fed mid, don't hesitate to build it, you might need it in team fights.

This item gives you some AD and a great amount of armor penetration.
You can build this item if the enemy builds a lot of armor or if you are really fed and want to kill the enemy even faster.

This item gives you some AD and magic resistance, but the reason you get this item is because the enemy team has much crowd control. Not much taken because most people don't know the item, or don't want to buy it because it's not cheap.

Some alternatives;

This items is a good item if you like the attack speed/movement speed buff from it's passive. Otherwise you can better get Black Cleaver.

This item is actually quite funny. It's has a nice passive AOE effect, and also a nice active AOE effect. The 75 Attack Damage is quite high, but it doesn't really fit in Riven's Tanky AD build.

This Item has a huge amount of HP but the passive slow is quite useless on a Riven who has a stun and a knock up ability. The attack damage is a bit low to be useful.

Honestly, I never used this item on Riven because I didn't even knew it existed. But if you read it, it's not expensive and has some nice statistics.
Also the passive is nice, your attacks deal 4% of the enemy's current health in physical damage and healing you half that amount.
And then the Active; Deal 150 Physical damage and 50% of your own Attack damage to the enemy and healing you for that same amount. How awesome is that?

This item is really nice if the enemy is stacking a lot of armor, it doesn't give much attack damage. There isn't much more to say about it.

I only use this item for snowballing, it has some nice statistics but the mana is useless and Riven doesn't need critical strikes.

I love this item so much, you can die 2 times every 5 minutes!
And it gives you Armor and Magic Resistance.

This item is a good Armor/Health item. It's passive is also nice.
Active, hmm, I actually never use it, but if you use it right it could be a life safer.

It's quite a nice item if you get focused a lot or if you go in the jungle a lot. Otherwise its not so good. The armor is pretty nice and the AOE DPS is nice too.

This item is nice if you want a bit armor, magic resistance and health, and also gives your teammates a small boost of Armor, Magic resistance and health regeneration/5.

--> It's the better version of the Aegis :)