I initially bought an iPad to have an easy way to do basic web stuff when my computer wasn't available. Since then, it has become a vital part of what I do every day in my music career. Here's my top 5 music related uses for it:
As a control surface
There are a bevy of free/low cost apps that instantly turn any iPad into a controller for your DAW or music plugin- my two favorites are RSTouch for controlling Reason, and the free app AB1818VSL (crappy name, great app) for controlling my Audiobox VSL audio interface. Just those two apps alone are worth getting an iPad- they completely replaced my old Mackie control surface.
As a sheet music reader
Being able to organize and store thousands of pages of sheet music in a light, easy-to-carry device makes gigging a breeze. I currently use ForScore because its amazing for organization and has a bunch of other cool options.
As a concert display
I use a slideshow on my iPad when I play small live shows to display my band's name and logo, and I even include a google number people can text to send us requests. I use a simple low-cost app called Slideshow to run it.
As a credit card machine
Using the free app Square, I can now take credit cards at my shows or for other odd jobs. The large touchscreen interface makes it easy to see what I'm charging people, and customers love that they can sign the screen to authorize their purchase.
As an instrument
Believe it or not, the iPad actually makes a pretty amazing synthesizer live. The SSD hard drive makes the latency almost inaudible, and some of the apps available are super powerful. My favorite app is Sampletank, which is a great all-around workstation synthesizer app. There's also a bunch of awesome analog synth emulators, including iMini, Korg's MS-20 emulation, and my personal favorite, Moog's Animoog.