I personally recommend
Cleartune. It's not a guitar-specific tuner, so if you don't know the name of each string (EADGBE), you will have a hard time. It's VERY accurate (within 1 cent, which is pretty much as good as it gets). It displays results in real time, which is AMAZING for a tuner.
I used it pretty much every day in university (I am a music student). It can detect notes from virtually any instrument. I used it for tuba (most tuners wont work for a tuba, but this one did).
It's only $3.99, which is a steal, considering actual tuners cost upwards of $20. It's the most accurate tuner my tuba professor has ever seen (and he's owned many expensive tuners. He loves how it displays results in realtime.
There is another app I had seen about a week back on the app store, called
Guitar Machine. If you're looking for a guitar-specific tuner, this might be your best bet. I don't own this app, so I can't vouch for what the developer claims, but they speak highly of it. It's on sale for $0.99, and is accurate within the sub-cent range (they claim it's the most accurate tuner on the app store). It also has guitar features like chord diagrams and a metronome. Great UI too.
Best of luck choosing an app that suits your needs. Let us know what you choose