PopChar has been around since nearly the dawn of time, at least in terms of the Mac operating system. PopChar started as a Turbo Pascal-based substitute for Key Caps, created on a Mac Plus way back in 1987. Its core functionality remains the same today, helping users insert unusual characters directly into documents--choosing from an increasingly arcane array of strange and foreign symbols, across thousands of Unicode-supported characters, all without having to learn any difficult key combinations.
Similar to the built-in Character Palette and Keyboard Viewer in OS X, PopChar X is accessed from your menu bar (or with an optional, customizable hot key), but it offers an easier interface and many more options than these built-in tools--including an always-on-top Favorites group, for frequently used characters. PopChar X auto-detects your current font, gives you a powerful search function across font boundaries, offers a variety of input methods, inserts HTML symbols, and more. A cool "reverse font search" even lets you know which fonts support a given character.
Overall, the only drawback to PopChar X is its price, but this app can still be a good value for anyone who uses its features frequently.