God = a title meaning "that which deserves to be worshiped."
Even though the term is sometimes used as a NAME for the myriad different gods that people have worshipped throughout history, the term God is not a name (like Yahweh, Elohim, Jehovah, Allah, Zeus, etc). God is a TITLE. And, as noted above, the title means "that which deserves worship."
Worship denotes obedience to, deference and awe toward, devotion and adoration of some being or some thing. In the past, people referred to their ruler, Pharaoh, or King as "your Worship." Of course, Kings and rulers used to be thought of as offspring of Gods, Gods themselves, or part-God. Nowadays, we don't think of Kings and rulers in the same way, and we therefore do not worship them anymore.
And the reason we don't feel it appropriate to worship mere mortal Kings or Presidents, despots or dictators, is that they lack qualities that God has. And the qualities that the God of ethical monotheism has to have, in order to earn the title of God, and merit any one's worship, include:
1. Omnipotence = God is not limited in power. God can do whatever God wants, or needs, to do.
2. Omniscience = There is no limit on God's knowledge. God knows everything.
3. Omniperfection = There is no limit on God's morality. God is all good, all loving, all-(any good moral quality). Fill in the blank. He is not limited or deficient in any moral quality.
4. Omnipresence = God's power or ability is not limited by space or distance. There is no corner of the universe that God's influence cannot reach.
5. Aseity = a big word philosophers use that means God is not dependent or subordinate to anything external to itself. He does not need to check in with, or get approval from anything else in the universe. He's the head-honcho.
Notice, that I can't help myself from using gendered terms for God. You can just ignore this gendered convention if you wish. God should be worshiped if it turns out to be a he, she, it, or something non-gendered. I'm just falling into the common convention of calling God a "He" (even though the idea is absurd when you consider the evolution of sexual organs).
It's also worth noting that most believers in the God of ethical monotheism (Jews, Christians, and Muslims) believe in this sort of God. Mormons believe in the God of ethical monotheism as well; intact with all the aforementioned OMNI qualities. At LDS.org, God is described as "the Supreme Being in whom we believe and whom we worship. He is all-powerful and all-knowing, and He is full of love, mercy, charity, and compassion. He is the Author of the plan for our happiness."
And God better have all these OMNI qualities, since a God that does not possess them would not be worth worshiping. For example, God would not deserve worship if he was not all powerful. Why worship a wimp, or even a very powerful yet limited being like an advanced extra-terrestial? An advanced alien life-force that has evolved for millions of years beyond us, and possessing some amazing technology, would surely appear to be all-powerful (just as I might appear all-powerful to my dogs). But this limited being would not be deserving of worship because, despite appearances (and really cool technology), it wouldn't be omnipotent. Therefore an advanced E.T. does not earn the moniker of God, nor does it deserve to be worshiped.
Second, a being that isn't all knowing does not deserve our worship. Why worship something that is not very bright? Again, go back to the E.T. argument. An advanced E.T. might be smarter than us, but not all knowing. It might not know the future, for example, and therefore wouldn't know the consequences of their actions (which might be catastrophic). Or they might not know anything about human beings, and therefore not know what is best for us. Whatever it is that they know (which would be much more than we do), they don't know everything, and therefore are undeserving of worship.
Third, a God deserving of worship would need to be all-perfect. If God was lacking in courage or love or goodness or any other moral quality, then worship is off the table. Why worship a being who could sometimes be cruel, petty, vindictive, or selfish? (Read the Old Testament for examples). This type of all-powerful being would be something of a dictator or tyrant. I wouldn't worship such a being, and neither should you; this sort of God is not deserving.
I almost want to skip omnipresence since it usually isn't emphasized. However, I will just say that if there is some corner of the universe or world that is beyond God's powers, or ability to travel to, then God has a blind spot of sorts, and isn't omnipresent. If God had to travel by spaceship across the universe, rather than instantaneously by some sort of God-magic, then again, God is limited.
And finally, my favorite word of the bunch: aseity. Aseity is a big ten-dollar word meaning that God is not dependent on anything else, like another God for example. For example, Mormons sometimes make the mistake of believing that God is checked in power by another God (maybe a God that existed before Him, since Mormons believe that God was once a mere mortal like we are). This sort of God does not have aseity, and therefore is not supreme. Why worship a non-supreme being? It would be more appropriate to worship whoever is supreme - not the one that is subordinate. Zoroastrians (a really old religion that predates Islam in the Middle East) believe in dualism, which is the idea that a good God is checked in power by an evil God. The two are locked in an eternal struggle for control of the universe. Asian philosophy and Confucianism have a similar idea in yin and yang. This almost sounds familiar to the LDS concept of God and Satan, except that Mormons think that God allows Satan to roam for a season to fulfill his purposes of providing an "opposition in all things," after which God will banish him.
So, God must have all these omni-qualities if worship is an appropriate response or attitude to take towards it. If God is shown to not have at least one of these qualities, then worship towards God is not an appropriate response. OK. Just needed to get that out there to define terms. That's all I have to say about that.
Next, we will look at the first argument for God's existence: the cosmological argument.