By now there is a considerable amount of WordPress code around that is meant to be re-used by other developers. Unfortunately there is little to none practical and solid information on it and generally you are stuck going through frameworks one by one until you find the first you like or think they all suck terribly (whichever comes first).
Let’s make community writeup on which frameworks and parent themes we really use and why.
Standalone framework for developers making their own parent themes. Highly modular with most of the features loaded on demand by custom add_theme_support() calls.
Long established parent theme (earlier versions were from before standalone Core release). Includes considerable amount of ready-made templates with more available for download separately.
Has multiple child themes available (both native and from other developers).