I was just mucking around in 10.2 and discovered a Character Input Palette. Go to the System Prefs, International panel, and under the Input Menu tab, select "Character Palette". Now you've got a nice little menu that lets you activate a floating window with all the characters divided up into their categories (Math, Arrows, Parentheses, Crosses, Stars/Asterisks, Ornamental Punctuation, Latin, Accented Latin, Digits, Greek, Cyrillic).
Granted, most of the more obscure characters are only included in the Lucida Grande font, but it's a great way to explore the expansiveness of Unicode.
[
Editor's note: When activated, the menu widget shows up at the right side of your menu commands; you can actualy see the icon in the screenshot posted with
this hint.]