Aggregate function in an SQL update query?

Use:

UPDATE table1
   SET field1 = (SELECT SUM(t2.field2) 
                   FROM TABLE2 t2 
                  WHERE t2.field3 = field2)

UPDATE t1
SET t1.field1 = t2.field2Sum
FROM table1 t1
INNER JOIN (select field3, sum(field2) as field2Sum
   from table2
  group by field3) as t2
on t2.field3 = t1.field3  

Or you could use a mix of JBrooks and OMG Ponies answers:

UPDATE table1
   SET field1 = (SELECT SUM(field2)
                   FROM table2 AS t2
                  WHERE t2.field3 = t1.field3)
  FROM table1 AS t1