Charm is a mobile character map. If you need a particular Unicode character quickly, just open Charm, type part of the character's name, and tap the character card. It will be copied to the clipboard and you can go back to what you were doing.
It's really useful with a shortcut to launch it from anywhere, but it works just fine without.
It works for maths symbols, foreign letters, obscure punctuation, snowman (for some reason) and many emoji. You have to know the correct Unicode name at first, but you can put your own name in once you've found it.
If you use a symbol a lot, or manually tell Charm to prioritise it, it will always appear at the top of any search that matches it. You can also 'downvote' symbols that annoy you.
The web version is free, but slower and can be data-heavy on mobile. Try it at http://www.andrewt.net/charm
Renaming and priority features require Honeycomb or later.
Header image uses elements from https://www.flickr.com/photos/grggrssmr/5057950151 by Greg Grossmeier.