SQL Case Expression Syntax?

What is the complete and correct syntax for the SQL Case expression?

The complete syntax depends on the database engine you're working with:

For SQL Server:

CASE case-expression
    WHEN when-expression-1 THEN value-1
  [ WHEN when-expression-n THEN value-n ... ]
  [ ELSE else-value ]
END

or:

CASE
    WHEN boolean-when-expression-1 THEN value-1
  [ WHEN boolean-when-expression-n THEN value-n ... ]
  [ ELSE else-value ]
END

expressions, etc:

case-expression    - something that produces a value
when-expression-x  - something that is compared against the case-expression
value-1            - the result of the CASE statement if:
                         the when-expression == case-expression
                      OR the boolean-when-expression == TRUE
boolean-when-exp.. - something that produces a TRUE/FALSE answer

Link: CASE (Transact-SQL)

Also note that the ordering of the WHEN statements is important. You can easily write multiple WHEN clauses that overlap, and the first one that matches is used.

Note: If no ELSE clause is specified, and no matching WHEN-condition is found, the value of the CASE expression will be NULL.

Considering you tagged multiple products, I'd say the full correct syntax would be the one found in the ISO/ANSI SQL-92 standard:

<case expression> ::=
       <case abbreviation>
     | <case specification>

<case abbreviation> ::=
       NULLIF <left paren> <value expression> <comma>
              <value expression> <right paren>
     | COALESCE <left paren> <value expression>
                { <comma> <value expression> }... <right paren>

<case specification> ::=
       <simple case>
     | <searched case>

<simple case> ::=
     CASE <case operand>
          <simple when clause>...
        [ <else clause> ]
     END

<searched case> ::=
     CASE
       <searched when clause>...
     [ <else clause> ]
     END

<simple when clause> ::= WHEN <when operand> THEN <result>

<searched when clause> ::= WHEN <search condition> THEN <result>

<else clause> ::= ELSE <result>

<case operand> ::= <value expression>

<when operand> ::= <value expression>

<result> ::= <result expression> | NULL

<result expression> ::= <value expression>

Syntax Rules

1) NULLIF (V1, V2) is equivalent to the following <case specification>:

     CASE WHEN V1=V2 THEN NULL ELSE V1 END

2) COALESCE (V1, V2) is equivalent to the following <case specification>:

     CASE WHEN V1 IS NOT NULL THEN V1 ELSE V2 END

3) COALESCE (V1, V2, . . . ,n ), for n >= 3, is equivalent to the
   following <case specification>:

     CASE WHEN V1 IS NOT NULL THEN V1 ELSE COALESCE (V2, . . . ,n )
     END

4) If a <case specification> specifies a <simple case>, then let CO
   be the <case operand>:

   a) The data type of each <when operand> WO shall be comparable
      with the data type of the <case operand>.

   b) The <case specification> is equivalent to a <searched case>
      in which each <searched when clause> specifies a <search
      condition> of the form "CO=WO".

5) At least one <result> in a <case specification> shall specify a
   <result expression>.

6) If an <else clause> is not specified, then ELSE NULL is im-
   plicit.

7) The data type of a <case specification> is determined by ap-
   plying Subclause 9.3, "Set operation result data types", to the
   data types of all <result expression>s in the <case specifica-
   tion>.

Access Rules

   None.

General Rules

1) Case:

   a) If a <result> specifies NULL, then its value is the null
      value.

   b) If a <result> specifies a <value expression>, then its value
      is the value of that <value expression>.

2) Case:

   a) If the <search condition> of some <searched when clause> in
      a <case specification> is true, then the value of the <case
      specification> is the value of the <result> of the first
      (leftmost) <searched when clause> whose <search condition> is
      true, cast as the data type of the <case specification>.

   b) If no <search condition> in a <case specification> is true,
      then the value of the <case expression> is the value of the
      <result> of the explicit or implicit <else clause>, cast as
      the data type of the <case specification>.

Here are the [CASE statement examples from the PostgreSQL docs][1] (Postgres follows the SQL standard here):

SELECT a,
   CASE WHEN a=1 THEN 'one'
        WHEN a=2 THEN 'two'
        ELSE 'other'
   END
FROM test;

or

SELECT a,
   CASE a WHEN 1 THEN 'one'
          WHEN 2 THEN 'two'
          ELSE 'other'
   END
FROM test;

Obviously the second form is cleaner when you are just checking one field against a list of possible values. The first form allows more complicated expressions.

[1]: http://www.postgresql.org/docs/current/static/functions-conditional.html "Conditional Expressions"

Sybase has the same case syntax as SQL Server:

Description

Supports conditional SQL expressions; can be used anywhere a value expression can be used.

Syntax

case 
     when search_condition then expression 
	[when search_condition then expression]...
	[else expression]
end

Case and values syntax

case expression
	 when expression then expression 
	[when expression then expression]...
	[else expression]
end

Parameters

case

begins the case expression.

when

precedes the search condition or the expression to be compared.

search_condition

is used to set conditions for the results that are selected. Search conditions for case expressions are similar to the search conditions in a where clause. Search conditions are detailed in the Transact-SQL User’s Guide.

then

precedes the expression that specifies a result value of case.

expression

is a column name, a constant, a function, a subquery, or any combination of column names, constants, and functions connected by arithmetic or bitwise operators. For more information about expressions, see “Expressions” in.

Example

select disaster, 
       case
            when disaster = "earthquake" 
                then "stand in doorway"
            when disaster = "nuclear apocalypse" 
                then "hide in basement"
            when monster = "zombie apocalypse" 
                then "hide with Chuck Norris"
            else
                then "ask mom"
       end 
  from endoftheworld

I dug up the Oracle page for the same and it looks like this is the same syntax, just described slightly different.

Link: Oracle/PLSQL: Case Statement

Oracle syntax from the 11g Documentation:

CASE { simple_case_expression | searched_case_expression }
     [ else_clause ]
     END

simple_case_expression

expr { WHEN comparison_expr THEN return_expr }...

searched_case_expression

{ WHEN condition THEN return_expr }...

else_clause

ELSE else_expr

Here you can find a complete guide for MySQL case statements in SQL.

CASE
     WHEN some_condition THEN return_some_value
     ELSE return_some_other_value
END

Case statement syntax in SQL SERVER:

CASE column
   WHEN value1 THEN 1
   WHEN value3 THEN 2
   WHEN value3 THEN 3
   WHEN value1 THEN 4
   ELSE ''
END

And we can use like below also:

CASE 
   WHEN column=value1 THEN 1
   WHEN column=value3 THEN 2
   WHEN column=value3 THEN 3
   WHEN column=value1 THEN 4
   ELSE ''
END