What operations result in automatic creation of SQL Server statistics? My understanding is that creating an index automatically creates statistics for that column.
What else results in auto creation of statistics? For example - Does SQL Server create statistics for every column that has ever appeared in a WHERE clause?
AUTO_CREATE_STATISTICS Option

When the automatic create statistics option, AUTO_CREATE_STATISTICS is ON, the Query Optimizer creates statistics on individual columns in the query predicate, as necessary, to improve cardinality estimates for the query plan.
These single-column statistics are created on columns that do not already have a histogram in an existing statistics object.
When the Query Optimizer creates statistics as a result of using the AUTO_CREATE_STATISTICS option, the statistics name starts with _WA.
You can use the following query to determine if the Query Optimizer has created statistics for a query predicate column.
SELECT OBJECT_NAME(s.object_id) AS object_name,  
    COL_NAME(sc.object_id, sc.column_id) AS column_name,  
    s.name AS statistics_name  
FROM sys.stats AS s 
INNER JOIN sys.stats_columns AS sc  
    ON s.stats_id = sc.stats_id AND s.object_id = sc.object_id  
WHERE s.name like '_WA%'  
ORDER BY s.name;


That includes WHERE predicate:
SELECT *
FROM tab
WHERE col = ?;    -- here tab.col

and JOIN predicate(to determine physical join type: NESTED LOOPS/MERGE/HASH):
SELECT *
FROM tab1
JOIN tab2 
  ON tab1.id = tab2.tab_1_id; -- here tab2.tab_1_id