Magento Repurchase Rate Note: This assumes you don't use guest checkout - if you do, you could probably group by customer_email and get relatively accurate results.

repurchase-rate.sql

# The number of customers who haveve only purchased once from December 2012 to December 2013

SELECT customers_in_segment
FROM
(
    SELECT count(*) AS customers_in_segment, order_count
    FROM 
    (
        SELECT customer_id, min(created_at) AS first_order_at, count(*) AS order_count
        FROM sales_flat_order
        WHERE created_at < '2013-12-31'
        GROUP BY customer_id
    ) AS summary
    WHERE first_order_at BETWEEN '2012-12-01' AND '2012-12-31'
    GROUP BY order_count
) AS summary2
WHERE order_count = 1

UNION

# The total number of new customers in December 2012
SELECT count(*)
FROM
(
    SELECT customer_id, min(created_at) AS first_order_at, count(*) AS order_count
    FROM sales_flat_order
    WHERE created_at < '2013-12-31'
    GROUP BY customer_id
) AS summary
WHERE first_order_at BETWEEN '2012-12-01' AND '2012-12-31'