Vim will show you the decimal, octal, and hex index of the character under the cursor if you type ga in normal mode. Keying this on an ASCII a character yields the following in the status bar:

<a>  97,  Hex 61,  Octal 141

This information can be useful, but it’s worth it to extend it to include some other relevant information, including the Unicode point and name of the character, its HTML entity name (if applicable), and any digraph entry method. This can be done by installing the characterize plugin by Tim Pope.

With this plugin installed, pressing ga over a yields a bit more information:

<a> 97, \141, U+0061 LATIN SMALL LETTER A

This really shines however when inspecting characters that are available as HTML entities, or as Vim digraphs, particularly commonly used characters like an EM DASH:

<—> 8212, U+2014 EM DASH, ^K-M, &mdash;

Or a COPYRIGHT SYMBOL:

<©> 169, \251, U+00A9 COPYRIGHT SIGN, ^KCo, ^KcO, :copyright:, &copy;

Or as one of the eyes in a look of disapproval:

<ಠ> 3232, U+0CA0 KANNADA LETTER TTHA

Note that ga shows you all the Unicode information for the character, along with any methods to type it as a digraph, and an appropriate HTML entity if applicable.

If you work with multibyte characters a lot, whether for internationalization reasons or for typographical correctness in web pages, this may be very useful to you.