WebView is definitely an option since it is essentially a web browser in a box, but like Mark said, it's a bit heavyweight and will cause a noticeable delay.
TextViews can handle basic HTML too, and if you're just looking for some simple formatting (bold, italics, color), then using the standard text view is the way to go.
It's important to know the difference between a String and a CharSequence (and Spannable) - Strings do not have HTML support, and if you grab a string from the resources (through Context.getString()), it will automatically strip out all HTML code. So you need to use Context.getText()).
In any case, here is an example:
new AlertDialog.Builder(this)
.setTitle("HTML Example")
.setMessage(Html.fromHtml("<b>Bold text</b> <i>and italics</i>"))
.setPositiveButton("Sweet")
.create()
.show();