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The problem is that you are not including the ID of the record to be deleted for each row--they all have the same id: "checkbox". You could make each check box name contain the record id, like: name=\"removeid[".$row[0]."]\" or whatever position the id is in your query. I would advise that you use mysql_fetch_assoc(), though, then extract(), so that you have all the variables with recognizable names, then you could do something like: name=\"removeid[$id]\". In your form data handling code, then you could just go through the $_POST['removeid'] array and you would have the record id's to be deleted.
The value that is submitted if the checkbox is checked is the "value=x" attribute rather than the "id=x" one. As far as I know the "id" attribute has no real meaning for a checkbox. See: http://www.echoecho.com/htmlforms09.htm
You're creating an array of checkboxes 0-x, but they bear no relation to your records. Califdon's suggestion is one way to do it, in which case you don't need a value for them. You will step through the array using the indexes of the array.
The other would be to go your route but use value attributes and set them equal to the record id. Then step through the array using those values.