How do I UPDATE from a SELECT in SQL Server?

UPDATE
    Table_A
SET
    Table_A.col1 = Table_B.col1,
    Table_A.col2 = Table_B.col2
FROM
    Some_Table AS Table_A
    INNER JOIN Other_Table AS Table_B
        ON Table_A.id = Table_B.id
WHERE
    Table_A.col3 = 'cool'

In SQL Server 2008 (or newer), use MERGE

MERGE INTO YourTable T
   USING other_table S 
      ON T.id = S.id
         AND S.tsql = 'cool'
WHEN MATCHED THEN
   UPDATE 
      SET col1 = S.col1, 
          col2 = S.col2;

Alternatively:

MERGE INTO YourTable T
   USING (
          SELECT id, col1, col2 
            FROM other_table 
           WHERE tsql = 'cool'
         ) S
      ON T.id = S.id
WHEN MATCHED THEN
   UPDATE 
      SET col1 = S.col1, 
          col2 = S.col2;

UPDATE YourTable 
SET Col1 = OtherTable.Col1, 
    Col2 = OtherTable.Col2 
FROM (
    SELECT ID, Col1, Col2 
    FROM other_table) AS OtherTable
WHERE 
    OtherTable.ID = YourTable.ID

I'd modify Robin's excellent answer to the following:

UPDATE Table
SET Table.col1 = other_table.col1,
 Table.col2 = other_table.col2
FROM
    Table
INNER JOIN other_table ON Table.id = other_table.id
WHERE
    Table.col1 != other_table.col1
OR Table.col2 != other_table.col2
OR (
    other_table.col1 IS NOT NULL
    AND Table.col1 IS NULL
)
OR (
    other_table.col2 IS NOT NULL
    AND Table.col2 IS NULL
)

Without a WHERE clause, you'll affect even rows that don't need to be affected, which could (possibly) cause index recalculation or fire triggers that really shouldn't have been fired.

One way

UPDATE t 
SET t.col1 = o.col1, 
    t.col2 = o.col2
FROM 
    other_table o 
  JOIN 
    t ON t.id = o.id
WHERE 
    o.sql = 'cool'