deleting orders & customers results in corrupted table 'field_data_commerce_unit_price'

You cannot just delete entities in Drupal 7. There's almost always going to be field data attached that you also need to clean up, not to mention revision data. You can do this through the UI on each item individually or use Views Bulk Operations to setup a View to do it all at once. The quick fix for you now would be to update your customer and order tables' autoincrement key to 1 higher than whatever you had before. The longer fix will be for you to empty out all the related field tables and clear your caches.

Any table with commerce in it would need to be truncated, whether it's for a Commerce entity or field. Don't forget the various revision tables, too.

I'm sorry, I don't have a list. There are other threads that do. If you need more help on this, try asking in #drupal-commerce on IRC.

Since this ranks high on google; I figured I'd help our fellow drupal commerce users with a good enough answer.

truncate commerce_order;
truncate commerce_order_revision;
truncate field_data_commerce_line_items;
truncate field_revision_commerce_line_items;
truncate field_data_commerce_order_total;
truncate field_revision_commerce_order_total;
truncate field_data_commerce_customer_billing;
truncate field_revision_commerce_customer_billing;
truncate commerce_line_item;
truncate field_data_commerce_product;
truncate field_data_commerce_unit_price;
truncate field_data_commerce_total;
truncate field_data_commerce_display_path;
truncate field_revision_commerce_product;
truncate field_revision_commerce_unit_price;
truncate field_revision_commerce_total;
truncate field_revision_commerce_display_path;
truncate field_data_commerce_customer_shipping;
truncate field_revision_commerce_customer_shipping;

my 2 cents

####	Delete all orders 

	truncate commerce_line_item;
	truncate commerce_order;
	truncate commerce_order_revision;

	truncate field_data_commerce_customer_address;
	truncate field_data_commerce_customer_billing;
	truncate field_data_commerce_customer_shipping;
	truncate field_data_commerce_display_path;
	truncate field_data_commerce_line_items;
	truncate field_data_commerce_order_total;
	truncate field_data_commerce_product;
	truncate field_data_commerce_total;
	truncate field_data_commerce_unit_price;

	truncate field_revision_commerce_customer_billing;
	truncate field_revision_commerce_customer_shipping;
	truncate field_revision_commerce_display_path;
	truncate field_revision_commerce_line_items;
	truncate field_revision_commerce_order_total;
	truncate field_revision_commerce_product;
	truncate field_revision_commerce_total;
	truncate field_revision_commerce_unit_price;

There is more cents to this :) (for my site setup)

truncate commerce_customer_profile;
truncate commerce_customer_profile_revision;
truncate field_data_commerce_shipping_service;
truncate field_revision_commerce_shipping_service;

truncate commerce_line_item;
truncate commerce_order;
truncate commerce_order_revision;

truncate field_data_commerce_customer_address;
truncate field_data_commerce_customer_billing;
truncate field_data_commerce_customer_shipping;
truncate field_data_commerce_display_path;
truncate field_data_commerce_line_items;
truncate field_data_commerce_order_total;
truncate field_data_commerce_product;
truncate field_data_commerce_total;
truncate field_data_commerce_unit_price;

truncate field_revision_commerce_customer_address;
truncate field_revision_commerce_customer_billing;
truncate field_revision_commerce_customer_shipping;
truncate field_revision_commerce_display_path;
truncate field_revision_commerce_line_items;
truncate field_revision_commerce_order_total;
truncate field_revision_commerce_product;
truncate field_revision_commerce_total;
truncate field_revision_commerce_unit_price;

Just wanted to say thank you, as this was a life-saver. I knew better than to manually mess with the Order tables... what was I thinking?

Thanks again!

Thank you Thank you Thank you Thank you Thank you Thank you Thank you Thank you Thank you . Just wasted three days on this. All fixed.

Thank you this is the best solution.

Latest Drupal 7.54 and Drupal commerce 7.x.-1.13 this still fixed my issue. Thank you!