When we accuse someone of "playing God," it is usually because of their forced intervention into events in order to achieve some kind of perfect plan they seek to execute. Well, this just isn't how God goes about things, though you could be forgiven for suspecting that some of the wonders of the world were planned in detail by a divine being.
The universe and everything in it was quite evidently not planned by somebody kind of like us but one heck of a lot smarter - God sitting at the Universal Computer plotting out all those microbes, molecules and chromosomes - making wood soft and iron hard, deciding where the mountains and deserts go, whether you catch your bus or not, and when your third baby tooth is due. If you were God, wouldn't you have better things to do? Wouldn't you build some handy labour-saving device into your system so you could chill-out sometimes and conceive new universes?
God, however you wish to perceive It, created a universe in which everything was free to create its own future. God does not work to a predetermined plan, but the Universe itself creates an order from the events that take place within it. The understanding of this in the new science of chaos theory shows us that when you have a large number of seemingly unconnected events flowing freely, they are much more likely to form relationships, a flowing stability and order than some mish-mash of mixed-up tangled relationships that don't work. This looks like a bona-fide universal rule, yet for a long time humankind has worked on the principle that order must be deterministically shaped from the chaos; order and stability created according to either our plan or our linear interpretation of God's plan. Today's mainstream God of Christianity and Islam is often perceived to have planned our world, and dictated down to specifics how we should behave.
Of course, it is the failure of these plans, God-given or man-made that is the most frequent cause of grief to our species. For reasons that we all innately understand, our reaction to the death of 1500 from an earthquake in Italy is dwarfed by the horrible shelling of 70 cafe-goers in the centre of Sarajevo or the bombing of a dancehall in Northern Ireland. We live on the earth and must accept that it has a destiny of its own that may or may not fit in with our city-siting plans and personal lifetime goals. But the cold technological killing of each other for the benefit of the eventually successful tax-collector, whether church, state, or terrorist seeking to be tomorrow's ruler, is so obviously not part of God's way that we shudder at a more visceral level.
Putting our trust in God and loving God are at the earliest core of many religious teachings, combined with the overall rule of showing consideration to others. Yet by the time this trust and love are filtered through central control they become obedience to the church's instructions and fear of the Lord should you disobey them. The great prophets sought to share their wisdom with us so that we might better pursue the path of being fulfilled and happy human beings. They sought to give us principles and thought tools, not preachers and rules.
God's power is based on allowing every element of creation to be free to create and enjoy its own destiny, in a universe which is somehow programmed to create order. We enjoy this order in everything from the delicate skin of our earth's atmosphere to the complex set of bacteria that protect our own skin and help us digest our food. This free system works, and when we use our considerable intellectual powers to construct an artificial structure that attempts to forcibly control the system, we are not playing at being God - we are denying and obstructing the greatest tool that God built into the universe.