_{The question is old but I felt the best answer hadn‘t been given, yet.}

Is there an UPDATE syntax ... without specifying the column names?

General solution with dynamic SQL

You don‘t need to know any column names except for some unique column(s) to join on (id in the example). Works reliably for any possible corner case I can think of.

This is specific to PostgreSQL. I am building dynamic code based on the the information_schema, in particular the table information_schema.columns, which is defined in the ISO SQL standard and most modern RDBMS (except for Oracle) support it. But a DO statement with PL/pgSQL code executing dynamic SQL is totally non-standard PostgreSQL syntax.

DO
$do$
BEGIN

EXECUTE (
SELECT
‘UPDATE b
 SET   (‘ || string_agg(quote_ident(column_name), ‘,‘) || ‘)
     = (‘ || string_agg(‘a.‘ || quote_ident(column_name), ‘,‘) || ‘)
 FROM   a
 WHERE  b.id = 123
 AND    a.id = b.id‘
FROM   information_schema.columns
WHERE  table_name   = ‘a‘       -- table name, case sensitive
AND    table_schema = ‘public‘  -- schema name, case sensitive
AND    column_name <> ‘id‘      -- all columns except id
);

END
$do$;

Assuming a matching column in b for every column in a, but not the other way round. b can have additional columns.

WHERE b.id = 123 is optional, to update only a selected row.

SQL Fiddle.

Related answers with more explanation:

• Dynamic UPDATE fails due to unwanted parenthesis around string in plpgsql
• Update multiple columns that start with a specific string

 

Partial solutions with plain SQL

With list of shared columns

You still need to know the list of column names that both tables share. With a syntax shortcut for updating multiple columns - shorter than what other answers suggested so far in any case.

UPDATE b
SET   (  column1,   column2,   column3)
    = (a.column1, a.column2, a.column3)
FROM   a
WHERE  b.id = 123    -- optional, to update only selected row
AND    a.id = b.id;

SQL Fiddle.

This syntax was introduced with Postgres 8.2 in Dec. 2006, long before the question was asked.
More details in the manual and this related answer on dba.SE:

• Bulk update of all columns

 

With list of columns in B

If all columns of A are defined NOT NULL (but not necessarily B),
and you know the column names of B (but not necessarily A).

UPDATE b
SET   (column1, column2, column3, column4)
    = (COALESCE(ab.column1, b.column1)
     , COALESCE(ab.column2, b.column2)
     , COALESCE(ab.column3, b.column3)
     , COALESCE(ab.column4, b.column4)
      )
FROM (
   SELECT *
   FROM   a
   NATURAL LEFT JOIN  b -- append missing columns
   WHERE  b.id IS NULL  -- only if anything actually changes
   AND    a.id = 123    -- optional, to update only selected row
   ) ab
WHERE b.id = ab.id;

The NATURAL LEFT JOIN joins a row from b where all columns of the same name hold same values. We don‘t need an update in this case (nothing changes) and can eliminate those rows early in the process (WHERE b.id IS NULL).
We still need to find a matching row, so b.id = ab.id in the outer query.

db<>fiddle here
Old sqlfiddle.

This is standard SQL except for the FROM clause.
It works no matter which of the columns are actually present in A, but the query cannot distinguish between actual NULL values and missing columns in A, so it is only reliable if all columns in A are defined NOT NULL.

There are multiple possible variations, depending on what you know about both tables.