DatabaseSchemaObjectExistsException

Huh. Somehow you seem to have a ctools table that already exists even though you don't have ctools installed. I'm not sure how you got into that situation.

You probably need to drop that table manually.

From a mysql prompt: DROP TABLE ctools_object_cache;

I have a feeling if you have this issue you may have similar issues with other tables.

Thus must be a core issue, because I get that error when I enable Rules (rule_config table). And, in researching the error, I see another who posted the error related to Ubercart.

I have a very extended D7 site build. Reinstalling with fresh db is a sucky option. If anyone has other suggestion.

Well, reinstalling just the module that's failing to activate may be okay, I hope?

Yep. So far, so good on that approach. Disabled Rules module, uninstalled through UI (parts applicable), manually dropped module tables, deleted module files; ran update.php. Reinstalled all.

There does seem to be an unaddressed underlying problem though. Because I now have found several references to this error, related to different modules. Seems a core issue -- although I have yet to find an issue addressing it there.

The problem is reproducing it, I think.

Enabling the corresponding_node_references module displays the error:
DatabaseSchemaObjectExistsException: Table corresponding_node_references already exists. in DatabaseSchema->createTable() (line 652 of /<mysite>/includes/database/schema.inc)

schema.inc is attempting to
/**
* Create a new table from a Drupal table definition.