Let's consider the ones you suggested:
—¿Puedes darme una cuchara?
What I probably would've said here is traer instead of dar. (As I always say, verb usage hinges upon the region you are.)
That being said, the aforementioned sentence does not sound that polite, so I'd say:
—¿Podrías traeme una cuchara?
There's no need, in this case, to say por favor since podría is already polite.
—Quiero un jugo de naranja
isn't polite, but it is not regarded as rude either; on another level, this works in contexts where you're directly speaking to a waiter/waitress.
To fix this, we can introduce the subjuntivo de cortesía:
—Quisiera un jugo de naranja. (Note that the form quisiese is also possible, but unnatural for this construction.)
This way, you don't need por favor and the request is polite.
In light of these, I'll list other expressions so as to make polite requests not including por favor:
—¿Me traerías una cuchara?
—¿Te molesto / Te puedo molestar con una cuchara?
—¿Me podrías traer un jugo de naranja?
—Me gustaría un jugo de naranja.
These, I feel, will be of interest to you.