There's this new app everyone is trying so I went and downloaded it too. Spoiler: this is one to grab if you're using a lot of special characters not included on the iOS keyboard. For developer Amit Jain, a heavy user of math symbols, the lack of a character viewer was so frustrating that he went and created his own on iOS.
On top of being a nice-looking gallery that you can use as a reference tool, Simbol includes a space for composing equations by selecting multiple symbols in the desired order. Since I'm more of a writing person, the key functionality for me is having those evasive symbols I keen using in my texts. The library includes Unicode, ISO, language characters, HTML, math, Greek and other special symbols. You'll be surprised how often I have to look for the em dash and the right arrow on [ClipMenu], not remembering the key combination — this will be very useful on the iPhone.
Doing translation work on the Mac is easy. Unfortunately, in real life I use a Windows machine, forcing me to switch between keyboard layouts or learn the key combinations like an animal. There are some non-existent consonants in English and the accentuated vowels you see in many European languages that can get a bit tricky to remember.
Although Simbol offers the option to copy the symbol in HTML and see its entity number, I would love a reminder of those numeric keypad combinations when I'm using Windows. Right now I use a piece of paper under the monitor with a dozen frequent characters I keep forgetting, but you know, Simbol is definitely nicer to look at and it's also free.