You can use $addToSet operator to check exist before append element into array.
db.tags.update(
{name: 'sport'},
{$addToSet: { videoIDs: "34f54e34c" } }
);
In this update statement example, mongoDB will find the TAG document which matches name == sport, and then check whether the videoIDs array contains 34f54e34c. If not, append it to the array.
Detail usage of $addToSet please read here.