This question assumes a Windows system.
For installed fonts, one can use Windows' Character Map to view the available characters of those fonts (with their Unicode codes). Even better is the "Symbol" view in Microsoft Office Word.
What can I use to view the available characters in fonts that I have not installed on my system? The only program I have found which lets me do anything with uninstalled fonts is Opicon, but it only displays a "sample text", not the available characters.