You can use $addToSet with the aggregation framework to count distinct objects.
For example:
db.collectionName.aggregate([{
$group: {_id: null, uniqueValues: {$addToSet: "$fieldName"}}
}])
Or extended to get your unique values into a proper list rather than a sub-document inside a null _id record:
db.collectionName.aggregate([
{ $group: {_id: null, myFieldName: {$addToSet: "$myFieldName"}}},
{ $unwind: "$myFieldName" },
{ $project: { _id: 0 }},
])