Here are the modules that I can remember having to re-enable so far:
Core
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* xml (for import, export, xmlrpc api, etc)
* zlib (for auto-upgrading and web-based plugin installs)
* gd (for thumbnails, as kchayka said)
Plugins
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* sessions (required by wp e-commerce)
I found what I needed: More Fields. There’s also Custom Field Template, but More Fields adds fields to the edit page with a more native feel and is more user friendly (imo).