Most documentation and GUI toolbar icons imply that the markup generated from _, *, __ and ** ist italics and boldface when it really is <em> and <strong> in HTML, which were intended as semantic elements for their presentational counterparts <i> and <b>.
Sometimes, emphasis is represented differently, e.g. by colors, small capitals, underlines, letter spacing or typeface changes. There are other phrases that are presented in italic or bold type according to traditional Western typography – for some of them there are even appropriate HTML element types, e.g. <cite> and <dfn>. It is probably unrealistic to cover all of them with simple markup consisting of one or two characters as prefixes and postfixes, so people will keep on using underscores and asterisks for stuff that is not meant to be emphasized.
Should an implementation rather offer switches to make either _ or * generate different tags or should it add new markup for that?
Overload existing syntax
_em_, __strong__, *i*, **b**
or
*em*, **strong**, _i_, __b__
to
<em>em</em>, <strong>strong</strong>, <i>i</i>, <b>b</b>
or, for instance,
<em>em</em>, <strong>strong</strong>, <cite>i</cite>, <dfn>b</dfn>
Introduce new syntax
One could, for instance, reuse Mediawiki’s syntax that employs apostrophes.
'one', ''two'', '''three'''
to
‘one’, <i>two</i>, <b>three</b>
or, per user or document option,
<q>one</q>, <cite>two</cite>, <dfn>three</dfn>