MySQL 5.5

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CREATE FUNCTION GetStringCount(strValue VARCHAR(4000), charValue VARCHAR(4000))
RETURNS INTEGER DETERMINISTIC NO SQL
BEGIN
  RETURN IFNULL((CHAR_LENGTH(strValue) - 
    CHAR_LENGTH(REPLACE(strValue, charValue, ''))) /
    CHAR_LENGTH(charValue), 0);
END
CREATE TABLE example (
  col VARCHAR(4000)
);

INSERT INTO example VALUES
  ('Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.'),
  ('At vero eos et accusam et justo duo dolores et ea rebum.'),
  ('Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.'),
  (NULL);

Records: 4  Duplicates: 0  Warnings: 0

SELECT GetStringCount('Hello', 'l');
SELECT GetStringCount('This costs 5$.', '$');
SELECT GetStringCount('This costs 5€.', '€');

GetStringCount('Hello', 'l')

2

GetStringCount('This costs 5$.', '$')

1

GetStringCount('This costs 5€.', '€')

1

SELECT *, GetStringCount(col, 'a') 
FROM example;

col
GetStringCount(col, 'a')

Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.
11

At vero eos et accusam et justo duo dolores et ea rebum.
3

Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.
8

null
0

CREATE FUNCTION GetStringCountB(strValue TEXT, charValue TEXT)
RETURNS INTEGER DETERMINISTIC NO SQL
BEGIN
  RETURN IFNULL(FLOOR((LENGTH(strValue) - 
    LENGTH(REPLACE(strValue, charValue, ''))) / 
    LENGTH(charValue)), 0);
END
SELECT GetStringCountB('Hello', 'l');
SELECT GetStringCountB('This costs 5$.', '$');
SELECT GetStringCountB('This costs 5€.', '€');

GetStringCountB('Hello', 'l')

2

GetStringCountB('This costs 5$.', '$')

1

GetStringCountB('This costs 5€.', '€')

1

SELECT *, GetStringCountB(col, 'a') 
FROM example;

col
GetStringCountB(col, 'a')

Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.
11

At vero eos et accusam et justo duo dolores et ea rebum.
3

Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.
8

null
0

col	GetStringCount(col, 'a')
Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.	11
At vero eos et accusam et justo duo dolores et ea rebum.	3
Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.	8
null	0