The characters allowed in a URI are either reserved or unreserved (or a percent character as part of a percent-encoding)

http://en.wikipedia.org/wiki/Percent-encoding#Types_of_URI_characters

says these are RFC 3986 unreserved characters (sec. 2.3) as well as reserved characters (sec 2.2) if they need to retain their special meaning. And also a percent character as part of a percent-encoding.

The full list of the 66 unreserved characters is in RFC3986, here: https://www.rfc-editor.org/rfc/rfc3986#section-2.3

This is any character in the following regex set:

[A-Za-z0-9_.\-~] 

I tested it by requesting my website (apache) with all available chars on my german keyboard as URL parameter:

http://example.com/?^1234567890ß´qwertzuiopü+asdfghjklöä#<yxcvbnm,.-°!"§$%&/()=? `QWERTZUIOPÜ*ASDFGHJKLÖÄ\'>YXCVBNM;:_²³{[]}\|µ@€~ 

These were not encoded:

^0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ,.-!/()=?`*;:_{}[]\|~ 

Not encoded after urlencode():

0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ.-_ 

Not encoded after rawurlencode():

0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ.-_~ 

Note: Before PHP 5.3.0 rawurlencode() encoded ~ because of RFC 1738. But this was replaced by RFC 3986 so its safe to use, now. But I do not understand why for example {} are encoded through rawurlencode() because they are not mentioned in RFC 3986.

An additional test I made was regarding auto-linking in mail texts. I tested Mozilla Thunderbird, aol.com, outlook.com, gmail.com, gmx.de and yahoo.de and they fully linked URLs containing these chars:

0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ.-_~+#,%&=*;:@ 

Of course the ? was linked, too, but only if it was used once.

Some people would now suggest to use only the rawurlencode() chars, but did you ever hear that someone had problems to open these websites?

Asterisk
http://wayback.archive.org/web/*/http://google.com

Colon
https://en.wikipedia.org/wiki/Wikipedia:About

Plus
https://plus.google.com/+google

At sign, Colon, Comma and Exclamation mark
https://www.google.com/maps/place/USA/@36.2218457,...

Because of that these chars should be usable unencoded without problems. Of course you should not use &; because of encoding sequences like &. The same reason is valid for % as it used to encode chars in general. And = as it assigns a value to a parameter name.

Finally I would say its ok to use these unencoded:

0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ.-_~!+,*:@ 

But if you expect randomly generated URLs you should not use punctuation marks like .!, because some mail apps will not auto-link them:

http://example.com/?foo=bar! < last char not linked

RFC3986 defines two sets of characters you can use in a URI:

• Reserved Characters: :/?#[]@!$&'()*+,;=

  reserved = gen-delims / sub-delims

  gen-delims = ":" / "/" / "?" / "#" / "[" / "]" / "@"

  sub-delims = "!" / "$" / "&" / "'" / "(" / ")" / "*" / "+" / "," / ";" / "="

  The purpose of reserved characters is to provide a set of delimiting characters that are distinguishable from other data within a URI. URIs that differ in the replacement of a reserved character with its corresponding percent-encoded octet are not equivalent.

• Unreserved Characters: A-Za-z0-9-_.~

  unreserved = ALPHA / DIGIT / "-" / "." / "_" / "~"

  Characters that are allowed in a URI but do not have a reserved purpose are called unreserved.

From here

Thus, only alphanumerics, the special characters $-_.+!*'(), and reserved characters used for their reserved purposes may be used unencoded within a URL.

This answer discusses characters may be included inside a URL fragment part without being escaped. I'm posting a separate answer since this part is slightly different than (and can be used in conjunction with) other excellent answers here.

The fragment part is not sent to the server and it is the characters that go after # in this example:

https://example.com/#STUFF-HERE

Specification

The relevant specifications in RFC 3986 are:

 fragment = *( pchar / "/" / "?" ) pchar = unreserved / pct-encoded / sub-delims / ":" / "@" unreserved = ALPHA / DIGIT / "-" / "." / "_" / "~" sub-delims = "!" / "$" / "&" / "'" / "(" / ")" / "*" / "+" / "," / ";" / "=" 

This also references rules in RFC 2234

 ALPHA = %x41-5A / %x61-7A ; A-Z / a-z DIGIT = %x30-39 ; 0-9 

Result

So the full list, excluding escapes (pct-encoded) are:

A-Z a-z 0-9 - . _ ~ ! $ & ' ( ) * + , ; = : @ / ?

For your convenience here is a PCRE expression that matches a valid, unescaped fragment:

/^[A-Za-z0-9\-._~!$&'()*+,;=:@\/?]*$/ 

Encoding

Counting this up, there are:

26 + 26 + 10 + 19 = 81 code points

You could use base 81 to efficiently encode data here.

These are listed in RFC3986. See the Collected ABNF for URI to see what is allowed where and the regex for parsing/validation.

The upcoming change is for chinese, arabic domain names not URIs. The internationalised URIs are called IRIs and are defined in RFC 3987. However, having said that I'd recommend not doing this yourself but relying on an existing, tested library since there are lots of choices of URI encoding/decoding and what are considered safe by specification, versus what are safe by actual use (browsers).

If you like to give a special kind of experience to the users you could use pushState to bring a wide range of characters to the browser's url:

var u="";var tt=168; for(var i=0; i< 250;i++){ var x = i+250*tt; console.log(x); var c = String.fromCharCode(x); u+=c; } history.pushState({},"",250*tt+u); 

You probably forgot these [\x{000ff}-\x{e007f}] and these [ء-ي] characters ( IDN )