All the gory details can be found in the current RFC on the topic:  RFC 3986 (Uniform Resource Identifier (URI): Generic Syntax)
Based on this related answer, you are looking at a list that looks like: A-Z, a-z, 0-9, -, ., _, ~, :, /, ?, #, [, ], @, !, $, &, ', (, ), *, +, ,, ;, %, and =.  Everything else must be url-encoded.  Also, some of these characters can only exist in very specific spots in a URI and outside of those spots must be url-encoded (e.g. % can only be used in conjunction with url encoding as in %20), the RFC has all of these specifics.