Before anything, you can also change Ignite for Teleport. Which will give you more roam potential and more map pressure.

This is a guide that I wanted to do because I love Ahri, and even when she got nerfed, she is still one of my comfort pick. She is now more skill reliable, but she's a really fun champ to use.

Make sure you leave comments. If you want me to add some other match ups, feel free to leave a comment.

Pros:
[*] Really mobile champion
[*] A lot of burst potential
[*] Safe pick in most lane due to mobility

Cons:
[*] Really roam dependant, unless she can kill her opponent
[*] Skillshot dependant

Versus Ability Power Midlaner

This is my standard build if I am versus an AP midlaner. I either get the boots first if I play versus a Lux, who is really skillshot dependant and that movement speed will allow me to avoid the poke. If I get Doran's Ring first, I would get the boots after the Fiendish Codex if I don't have enough money for Needlessly Large Rod when I back, if I have the money I'll get the large rod instead. If not, I get the boots and get the items in this order.

Versus Attack Damage Midlaner

The difference with the other build is when I get the Zhonya's Hourglass. In a AD matchup I either get the Deathfire Grasp first or Zhonya's. It really depends on how aggressive the other midlaner is. If I'm getting destroyed, I will get zhonya. If I'm doing fine, I will try to get the Deathfire Grasp first and then [[zhonya's hourglass]. Since Zhonya gives me armor, it'll help me defend versus the opponent midlaner and at the same time help me do damage due to the 120 Ability Power.

Variations

There is a lot of variations possible, especially for the last item. Instead of Guardian Angel you can either go Rylai's Crystal Scepter for more health, ability power and more chase potential due to the passive on Rylai.
Instead of either of those, you can also get Banshee's Veil which is useful in a case where the other team is just trying to poke you down, before engaging. Banshee's will block the poke and when they will engage, you will be full health.

Versus Ability Power Midlaner

This is my runepage if I go versus a AP midlaner like , and others like that. It simply means, champions with skills that scales with ability power.
The Greater Glyph of Magic Resist will help me not die in the early levels. It's always something that you want.
The Greater Seal of Armor are just good against auto attacks and if you get ganked. So they are needed.
You want to get the Greater Mark of Magic Penetration because it gives more damage than the Greater Mark of Ability Power.
For the quintesseces, it's just the opposite of the marks. Greater Quintessence of Ability Power will do more damage and be more useful then Greater Quintessence of Magic Penetration

Versus Attack Damage Midlaner

This would be my runepage if I'm against a AD match up in the midlane. Since I don't need Greater Glyph of Magic Resist, I will take that opportunity to get Greater Glyph of Scaling Ability Power and get about 30 more Ability Power in the late game. The only difference is replacing Greater Glyph of Magic Resist with Greater Glyph of Scaling Ability Power.

Spell Order

I want to get Charm first cause that will do magic damage and allow me to auto attack him a few times for even more damage.
I prefer maxing Orb of Deception first because that will give me more poke damage and easier time clearing waves of minions. I then proceed to max Fox-Fire cause it has good utility in clearing waves as well as team fights. It does more damage than your Charm.

In the early game, you simply want to kill as many minions as you can. You just want to be careful for the ganks before you hit level 6.
If you can, try to harass your opponent. That will help you in the long run since you will force him back and will then be able to push the lane and roam.

As an assassin, you don't want to engage the fights yourself, unless you see an important target out of position that you could charm and burst down. If you can'T do that, let your team engage and try to come in the fights from the side. Charm whoever is near you and use the active of Deathfire Grasp to burst him down.

is obviously not that easy to play since she's an assassin, but played correctly, she can be deadly. All you need to watch for is not be out of position to get killed first. Because then your team loses a lot of kill potential.

Katarina is a matchup that I would consider favorable. Since she's melee, her only way to poke you without taking damage in return is her Bouncing Blades. So all you need to watch for is when she uses it. When she does, just move away of the minions if she used it on them, if it's on you, poke her back with Orb of Deception or, if you can, Charm. If she ever use her Shunpo, that's when she doesn't have any escape anymore, so you can now try to charm her to do as much damage as you can. If she ever come close to you and use her ultimate, Death Lotus, move away with your own ultimate, Spirit Rush, and try to charm her. If you land it, not only it will stop Kat's ultimate, but you will now do a 20% increased damage on her.

Zed is a tough match up. Yes he is melee, but the simple fact that he uses energy instead of mana makes him hard to lane against, and you need to be careful once he hits level 6. Avoid the poke. If he uses Living Shadow near you, move away and avoid his incoming Razor Shuriken. If you get too low in HP, he will try to all-in you and kill you. So try to avoid as many poke as you can.

This is a match up that I would consider hard in the early levels, but okay once you get your ultimate. He won't be able to poke you down like zed since his Void Spike doesn't go through targets. So stay behind your minions, farm as much as you can and avoid being isolated. Kha'zix Leap doesn't have a huge range, so you can stay in safe range while hitting all the minions. If you have a chance, Charm him and then use your other abilities to hit him. DO NOT use Spirit Rush unless you know you can kill him. Because if you are isolated, and you can't kill him, and you don't have your ultimate, that is when you'll be in trouble.

This is a match up that you can win early, before he gets a lot of gold. Since gragas scales better than you, you will need to apply pressure early game to make him lose as much minions as possible. The more you deny him farm, the better it'll be, since you will delay his damage.

This is another skill match up. The difference is that Leblanc is more snowball dependant than you. If she can't get enough damage fast enough to instantly kill a support or a AD carry, then she is useless. She doesn't have a whole lot of utility in a team fight unless she can delete someone. So you want to try to deny her farm and if she roams to a lane, roam with her. Deny her kills and tell your lanes to be careful when you can't see her.