One of my teachers used to say (minus a lot of removed swear words) If it ain’t in tune, it ain’t nothin’. With that in mind, two favorite tuners for the iPhone:
iStrobosoft by Peterson recreates their great tuner which used a strobe light and a spinning wheel to create a great harmonically rich visual display. This iPhone app is an awesome recreation and works superbly, giving you both fine and gross indicators as well as that awesome harmonic stack. You can calibrate it for accuracy, it supports capos and dropped tunings and other reference pitches, has a noise filter, an input boost, and some display settings.
The other is the polytune from tc electronic. Aimed at guitar players, it allows you to tune all six strings at once, a quick strum is all you need. Start fine tuning one string and the display switches to a finer display along with the pitch. It allows for drop tunings, a range of reference pitch (lots of folks don’t use 440 as the reference) and has a setting for bass players as well. there’s a couple of display settings for good measure.
Both of these guys support the mic on a phone so tuning an acoustic guitar only requires a somewhat quiet room.
Both are recommended and work really well. It’s great to have a such great tuners with me all the time.