Here are some of the iOS apps I have used when running role-playing games.
Goodreader: Good reader is a PDF (and other types of files) viewer. You can have several PDFs open at the same time and easily flip between them. It now even lets you have multiple tabs viewing different pages in the same PDF. You can add your own bookmarks to PDFs that lack them.
I have even used the annotation features to stock a map, which works OK.
Evernote: I have an RPG notebook in Evernote. I have tags for monsters, encounters, treasures, house rules, campaign ideas, setting ideas, preparation tips, and more.
UX Write: All my campaign notes are stored on Dropbox. UX Write is my word processing app of choice for viewing/editing them on iOS. One of the nice things about UX Write for this is its automatically populated outline that makes it quick to jump to the part of a document you need.
Dropbox: Besides keeping all my campaign notes in Dropbox, I also use it to share documents and images with my group. e.g. When the PCs discover a map, I may hand them a paper copy, but I also pull up the Dropbox app and copy it from my campaign notes into the shared folder.
Battle Map 2: I’ve experimented with using Battle Map 2 on a TV. Also used it a few times when one or two players were telecommuting to a game. It worked OK, but it wasn’t great.
Hex Map Pro: I’ve tried using this one on a TV too. Also wasn’t great.
Old School: This is an app for planning and running classic D&D combat encounters. I have only actually used it a couple of times, but it worked well.
Lotto Machine: This was created to randomly pick lotto numbers. You tell it the range of possible numbers and how many to choose. You have six PC and need them in a random order for some reason? You can make everyone roll a die and reroll ties. Or you can tell Lotto Machine that you need 6 numbers from 1 to 6. Need to randomly pick three of the PCs for some reason? Ask for 3 from 1 to 6.
InitiativeBoard: I haven’t actually used this one yet, but it looks handy for tracking individual initiative in any game.