This is the build I use for myself when playing Ahri. It is extremely effective in lower level play, but relies heavily on Ahri's skillshots. It will take some time to get good at Ahri, but once done you can run away with games with relatively little farm.

Required:

Flash - this summoner spell is critical on Ahri. When coupled with her ultimate, Ahri has unparalleled control over her positioning. Positioning is everything on Ahri, and Flash will help you in ganking, counter-ganking, laning, and team-fighting.

OR

Ghost - Those that don't have or don't like Flash should choose Ghost instead. You probably don't want to take Flash and Ghost though. Ghost is a decent alternative that doubles as an effective chase tool.

Recommended/Good

Ignite - Very helpful against Magic Resist. People will build MR just to counter you, and Ignite will eat right through it to get those kills throughout the game.

Exhaust - Good for countering an opposing AD carry, for getting early kills, and for ganks. I don't typically take it but it is certainly a valid choice.

Ignore

Smite, Clarity, Cv, Surge, Promote, Revive, Heal, Cleanse, Teleport