SOLVED - see Bish below
I've got a list of checkboxes that all dump to $fruitid, and a many-to-many table1:
SELECT boxid FROM table1 WHERE fruitid=$fruitid1 AND fruitid=$fruitid2 AND etc.
Building on the current suggestions, you should be able to get what you're looking for by simply adding GROUP BY and HAVING clauses:
SELECT boxid FROM table1 WHERE fruitid IN ($fruitid1, $fruitid2, ...) GROUP BY boxid HAVING COUNT(*) = $selectedFruitCount;
By grouping by boxid and adding the COUNT(), you get the number of 'interesting' fruits that each box contains. If that count equals the total number of fruits that were selected, then that box must contain each of the selected fruits (and possibly more). Keep in mind that this assumes that the combination of boxid and fruitid is unique.