And of course you can increment a field as shown there.
You can do a lot more than that:
UPDATE sometable SET field1 = field1 + 1 + IF(field2 > 3, 7, -12 )
WHERE id = 9102 AND field1 < 1000000
and so on and so on.
Heck, you can even "tack on" to text fields:
UPDATE sometable SET ticks = CONCAT( ticks,'*') WHERE id = 1817
That would make the ticks
field grow by one "*" every time the UPDATE is executed.