I got an iphone for Christmas, and now that I've run one show completely using it, I feel like I can weigh in with which apps I have found most useful-
Todo List
I really like this app- I did my preshow & postshow lists with it (hard copies in the book, of course) and LOVED it. It wasn't free ($1.99 maybe?) but totally worth the price tag, I think. You can keep multiple lists (I had one for preshow & one for postshow), and within the list you can make notes on individual tasks, color code, and sort by priority (I divided my preset list in half- "preset before house open" and "preset after house open"). I just check off the tasks as I go, and they don't get deleted- they just move down to a separate "completed tasks" section, so then when it's time to start preshow the next day I go back in and uncheck all the little boxes, and voila! So much easier than lugging around a clipboard, using a laminator, etc. Greener, too!
Time Adder
I read this thread & got the time adder app, and I've used it pretty regularly to add up overtime hours & to give a rough estimate of a run time when we've blocked scenes individually but haven't actually run the show yet. Pretty useful.
HeyTell
Basically it turns your phone into a walkie-talkie. You record a message by holding the button & speaking, and it pops up on the other person's screen like a text message alert; they can listen to the message by just clicking on it. It's faster than typing out a text message. The rest of the SM team at my theatre discovered it during the prep for the first tech of a show where we were all scrambling around trying to get props moved form the rehearsal room to backstage and sorted out & such, and it was really useful. Use the iphone headphones with the little microphone & you're like a secret agent, I swear. Also a free app.
ShopShop
Not strictly a stage management app, but I probably use it more frequently than any other app. It's a grocery list app- you can keep multiple lists (I have one for groceries and one for everything else) and every item you type into the list is saved in a master database. You can go in and edit out one-time purchases, but then it makes typing in a grocery list really easy, because everything you buy on a regular basis is already saved. I am prone to forgetting what I needed to buy by the time I actually make it to the grocery store, so this way I just have a constant grocery list going & I add things as I think of them. Best of all, it was free!