DROP TRIGGER [IF EXISTS] [schema_name.]trigger_name
This statement drops a trigger. The schema (database) name is
optional. If the schema is omitted, the trigger is dropped from
the default schema. DROP TRIGGER
requires the TRIGGER privilege for
the table associated with the trigger. (This statement requires
the SUPER privilege prior to MySQL
5.1.6.)
Use IF EXISTS to prevent an error from
occurring for a trigger that does not exist. A
NOTE is generated for a nonexistent trigger
when using IF EXISTS. See
Section 12.7.5.42, “SHOW WARNINGS Syntax”. The IF EXISTS
clause was added in MySQL 5.1.14.
Triggers for a table are also dropped if you drop the table.
When upgrading from a version of MySQL older than MySQL 5.0.10
to 5.0.10 or newer—including all MySQL 5.1
releases—you must drop all triggers and re-create them.
Otherwise, DROP TRIGGER does not
work for older triggers after the upgrade. See
Section 2.13.1.1, “Upgrading from MySQL 5.0 to 5.1”, for a
suggested upgrade procedure.

User Comments
We really need the "IF EXISTS" functionality. However, we are currently using 5.0.22. So, I came up with the example below. It is a bit complicated because of the lack of anonymous block support.
DROP TABLE IF EXISTS foo;
CREATE TABLE foo(i INTEGER);
DROP PROCEDURE IF EXISTS foo_trigger_deleter;
DELIMITER //
CREATE PROCEDURE foo_trigger_deleter
()
BEGIN
DECLARE l_count INTEGER;
SELECT count(*)
INTO l_count
FROM information_schema.TRIGGERS
WHERE TRIGGER_NAME = 'foo_trigger_deleter';
IF (l_count > 0)
THEN
DROP TRIGGER foo_trigger_deleter;
END IF;
END//
DELIMITER ;
call foo_trigger_deleter();
DROP PROCEDURE foo_trigger_deleter;
CREATE TRIGGER foo_trigger
BEFORE INSERT ON foo
FOR EACH ROW
SET NEW.i = NEW.i + 1;
@Kevin Regan
Supposing one can have several similar schemata (like dev, test, etc.), I think it's better to include the schema in the where clause of the select checking trigger existence:
SELECT count(*)
INTO l_count
FROM information_schema.TRIGGERS
WHERE TRIGGER_NAME = '<trigger_name>'
AND TRIGGER_SCHEMA = SCHEMA();
Combining the ideas from the last two comments, a block of code that will delete ALL triggers from the current schema:
-- Drop all triggers in current schema.
DROP PROCEDURE IF EXISTS trigger_deleter;
DELIMITER $$
CREATE PROCEDURE trigger_deleter()
BEGIN
DECLARE done INT DEFAULT 0;
DECLARE cur_trig_name VARCHAR(64);
DECLARE trigs CURSOR FOR
SELECT TRIGGER_NAME
FROM information_schema.TRIGGERS
WHERE TRIGGER_SCHEMA = SCHEMA();
DECLARE CONTINUE HANDLER FOR NOT FOUND SET done = 1;
OPEN trigs;
SET done = 0;
drop_loop: LOOP
FETCH trigs INTO cur_trig_name;
IF done THEN
LEAVE drop_loop;
END IF;
DROP TRIGGER cur_trig_name;
END LOOP;
SET done = 1;
CLOSE trigs;
END$$
DELIMITER ;
call trigger_deleter();
DROP PROCEDURE trigger_deleter;
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