Finding columns that are NOT NULL in PostgreSQL

No.

This query

SELECT DISTINCT column_name, table_name
FROM INFORMATION_SCHEMA.COLUMNS
WHERE column_name IS NOT NULL

will return all the rows that have a value in the column "column_name".

All rows in that table will always have a value in the column "column_name".

Do you just need to know how many columns are nullable and how many are non-nullable?

SELECT is_nullable, COUNT(*)
FROM INFORMATION_SCHEMA.COLUMNS
GROUP BY is_nullable;

Count by table name? I think you can use this.

SELECT table_name, is_nullable, count(*)
FROM INFORMATION_SCHEMA.COLUMNS
GROUP BY table_name, is_nullable
ORDER BY table_name, is_nullable;

To get a count of all NOT NULL columns in any table, use:

SELECT count(*)
  FROM information_schema.columns
 WHERE table_schema = 'table_schema_here'
   AND table_name   = 'table_name_here'
   AND is_nullable = 'YES';

I hope this will help someone.

To get a count of all NOT NULL columns:

SELECT count(*)
  FROM information_schema.columns
  WHERE  table_name  = 'table_name'
     AND is_nullable = 'NO';