Allowed symbols/characters in Minecraft chat
Minecraft officially supports ASCII characters under 0x80. It can render more characters, but they do not render correctly.
The supported characters are listed below.
!\"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_'abcdefghijklmnopqrstuvwxyz{|}~⌂ÇüéâäàåçêëèïîìÄÅÉæÆôöòûùÿÖÜø£Ø׃áíóúñѪº¿®¬½¼¡«»
You can find this list together with more info about the possibilities( colors, and style) of the chat at the Chat article on the MinecraftCoalition wiki, if figuring out what these characters are is too much trouble.
Minecraft chat now accepts 255 characters (a few still do not render correctly). Navigate to the Font section of the Wiki page and click expand to see the full list.
The current answer by Krael is out of date and wrong: even the old version contained several characters outside of ASCII. ASCII does not contain accented characters. Instead, Minecraft used to support windows-1252. There are 256 code points in it, of which 5 are unused, and 32 are control characters, leaving 219 characters.
Since Minecraft is an international game, it has since been modified to use a more extensive character set instead. Specifically, the old windows/java variant from ~2000 of unicode, UCS-2. This set contains 64K (65535) code points, a code point is not a character, including what's needed for basic communication in most popular spoken languages. Some South-east-asian scripts are missing and CJK-support is incomplete (variant forms, names, older glyphs missing). Note that not all these code points can be printed as a character; there's reserved spaces, control characters, and a whole host of historic artifacts I will not go into in this post; Unicode is incredibly complicated. The exact behaviour of minecraft with regards to all sorts of special code points is undocumented.
See the relevant wiki page. Minecraft has two font files. The regular font, and the unicode font.
The regular font contains a total of 2,374 characters in 3 files, and matches the older bitmaps in shape and style.
The so-called "unicode" font is in another set of files. Any character that cannot be looked up in the regular font files is instead retrieved from this set of files (unicode_page_nn.png). This font is less bolded to be able to support more detailed characters such as complex CJK glyphs.