If you believe in a god or gods, do you worship them?
Yes.
If you worship them do you do so because they demand it or because they deserve it, or both?
Both.
I have a hard time understanding why any being would want worship. If I were a genius roboticist and created a race of sentient robots I wouldn't ask for their worship but rather hold them as my equals. I can't put myself in a god's shoes that asks for worship and get it to make sense to me... any insights?
Well, a human being created a race of sentient robots isn't quite the same thing. God is worthy of worship not only because He created human beings, but because He created the entire universe, and everything within it, from nothing, and powers it with the energy of his own being. Because God is Infinite, eternal, trasncendant, immanent, omnipresent, omnipotent, omniscient, and utterly and essentially majestic, awesome, glorious, and sublime.
Edit: I guess a helpful definitional question should also be included: what is worship? Is there a difference between worship and great respect? What's the deal with some religions and the bowing of knees and the feudal-esque lordship of God?
It is important to note that worship (at least in Jewish thought) does not equal self-abasement, groveling, or mere begging.
Jewish Worship involves three aspects: Praise, Request, and Thanks. Praise is celebration of God's good deeds, his miraculous creation of Heaven and Earth, His kndness in freeing us from slavery in Egypt, His faithfulness in keeping promises He made to our ancestors, and His boundless generosity in establishig with us an eternal covenant. Request involves not only personal petitions, but our communal beseeching of God to help us be better people, to aid those in need of help, to help us achieve a repair and healing of the world, and that, just as He was faithful to the promises made to our furtherst ancestors, He be faithful to the promise of one day sending us the messiah. And Thanks involve not only thanks for our lives, our world, our boundless opportunities, our families and friends, and other good things we have, but for the things God does that we may not know about, that God will do for us in the future, and that God has done for our ancestors through the years.
At least for us, while worship can certainly be solemn, it is mostly joyful, a way we are glad to communicate with God, a way that gives us an opportunity to come together as a community to connect with our ancestors and descendants in a neverending cycle of gratitude for our existence, joy in our Covenant, and faithfulness to the One who has been faithful to us.
Things like bowing, or even occasional prostration, are not expressions of abjectness, they are gestures acknowledging the majesty and the grandeur of the Creator of the Universe. Images of God as king, queen, lord, father, mother, etc. are anthropomorphic metaphors, giving us concepts to which we can relate that are have a grain of similarity, in minature, to ourselves as created beings, and our relationship to the creator, protector, and reshaper of all things.