Recently on the Unicode list someone asked basically what the biggest number of combining characters could happen in a sequence.  It's as many as someone wants to use, though the normalization UTS15 adds a limit, and the font rendering problem gets weird.

An interesting example appeared on the list:

In Tibetan and Ranjana scripts there is a well known grapheme cluster or vertical stack (HAKṢHMALAWARAYAṀ) which consists of nine characters that stack vertically:

 

ཧྐྵྨླྺྼྻྂ U+0F67 U+0F90 U+0FB5 U+0FA8 U+0FB3 U+0FBA U+0FBC U+0FBB U+0F82

 

 

It is likely that there exist a few combinations even longer.

Hope that's interesting

-Shawn