Symbols is a really simple and well-executed app for iPhone and iPad developed by Rinat Khanov that offers easy access to over 2000 special characters.
Symbols, as the name suggests, contains a huge database of text symbols that you’d want to use. The symbols in the app are sorted by category and copying them is as easy as tapping on them. The categories include Arrows, Math, Emoji, Pictographs, Bullets/Stars, Technical, Punctuation, Letterlike & Enclosed. Tapping and holding down on a symbol marks it as Favorite and that is then available under the ‘Favorites’ listing. Your recently used Symbols are also easily accessible under ‘Recent’.
Symbols is a Universal app and supports iCloud Sync, so your Recent and Favorites are synced across your devices. Symbols is available on the App Store for just $0.99. I do wish there was a notes/scratchpad area in the app that let me compose a string without leaving the app, but I’m sure the dev would be adding it in an update.
Update: Version 1.2 — Released Dec 3rd, 2014
Version 1.2 of Symbols has just been released on the App Store. With this update, all the symbols available in the app are now available through a System keyboard that you can enable from your Settings. If you Allow Full Access, your characters stay in sync across all your devices.