The following apps are for teacher use only. Perhaps I'll do a "Student app" that I use with students. This list is by no means conclusive, just highlighting some of my more frequently used apps. All of these apps listed can be purchased through Apple's App store.
Notebook by Circus Ponies has made it's way up to the top of my list as well. Again, a bit on the pricey side, I was hesitant to download it, due to the unfavorable reviews. However, this also has a sister application for your Mac computer and can be synced using DropBox. This app lets me take notes on the fly, record the speaker to review later, drag in a neat link that fits nicely with a thematic unit, as well as different snapshots on the web.
Mobile Mouse: This has been a life saver so many times! This allows my iPhone to become a remote control for my computer while I facilitate around the room. Many times we'll use the 'close proximity' position to encourage on task behavior, but it's hard to do when having to run back up to the computer. Mobile mouse allows me to do more than navigate through powerpoint or keynote, I can do whatever I need to do from the back of the room, as if I were right at the computer. Love it!
Teacher's assistant: Absolutely love this one! Since I carry my iPad and iPhone pretty much whereever I go, this app has replaced the big bulky clipboard I used to use to 'take names' of off task students. This application allows me to annotate behavior, both positive and negative, and keep a record all through the school year. At a moment's notice, I can email the file of a single student to the parent and or administration with everything noted, when the infraction took place, what the infraction was, what my reaction to the response was, and even the time of day. It's a beautiful thing! No more torn notes or stickies to lose!
Teacher Pal: I've not used this one too much. I hope to utilize it more this upcoming school year. It has some of the same usefulness that Teacher's assistant has, except you can also use this to take role with. The plus to this, is that it's free! It has a cute interface and the set up is easy to use. This might be what fits your needs if you don't need all the bells and whistles of Teacher's assistant.
Seatcharter: My relief of this past year! Once I set my class up on this app, I was able to move students around until the seating arrangement satisfied me. There were several students that did not work efficiently when sat next to certain classmates, and it often took a while to rearrange the seating. This app has a simple but efficient interface. It also helps me to decide how to set up my room--it allows the addition of desks, people, text, cabinets, tables, and several other icons.