Codepoints: An Encyclopedia of Unicode Characters

http://codepoints.net/

From the home page:

Codepoints.net is dedicated to all the characters, that are defined in the Unicode Standard. Theoretically, these should be all characters ever used. In practice Unicode has 110181 codepoints defined at the moment, mapping characters from Egyptian Hieroglyphs to Dingbats and Symbols. 

All codepoints are arranged in 16 so-called planes. These planes are further divided into several blocks with Basic Latin being the first one. You can browse one by one by starting with the first codepoint, 0000 or search for a specific character. If you’re not fully sure, try “Find My Codepoint”, to narrow down the candidates. Or maybe you are more daring and want a random codepoint?