Drawing each accented glyph separately is too much work for the user and makes it too difficult to get the base glyphs to match. Composites should be composed from base glyph + accent, then only the accents need to be drawn.
The following accents are needed to cover most languages. (Source:
Letter Database).
Grave, acute, tilde, diaeresis, cedilla, ring, circumflex, caron, breve, macron, ogonek, double acute, dot above (Polish), combining comma above right (Czech), middle dot (Catalan),
Then for those characters that don't work with composites, you need Ææ Øø (for Danish, Norweigan), Ðð Þþ (Icelandic), Łł slash (Polish), Œœ (French), and perhaps a few more.