Insert a row into the table omitting all values? Suppose I have a table with a serial as primary key and couple of other columns, that are all nullable. Is there any way to insert a new row in that table by omitting all the columns in the insert clause? Since serial is auto-incremental and can be omitted right? The rest of columns can be null and can therefore be omitted too? So theoretically it should be possible somehow. But is it?
Yes, you can use the default values clause (at least in Postgres):

insert into some_table
default values;


Online example