Query below lists all schemas from all databases on SQL Server instance.

Here you can get list of databases only: link

Query

declare @query nvarchar(max);

set @query =
(select 'select ''' + name + ''' as database_name,
                name COLLATE DATABASE_DEFAULT as schema_name 
         from ['+ name + '].sys.schemas union all '
  from sys.databases 
  where database_id > 4
  for xml path(''), type).value('.', 'nvarchar(max)');

set @query = left(@query,len(@query)-10) + ' order by database_name, schema_name';
execute (@query);

Columns

• database_name - database name
• schema_name - schema name

Rows

• One row represents one schema within database
• Scope of rows: all schemas from all databases on SQL Server instance
• Ordered by database name, schema name

Sample results