The first thing I do for my home campaigns is strip out the part of the cleric class that says they get their powers from a god. They think they get their powers from a god, and they sure seem to have good proof of it, but most everyone not of that religion would disagree.
In my world, the religions don't mesh, just as they don't mesh in the real world. Sure, there may be some over-God who is perceived in aspects of all the other gods of various pantheons, but most members of any given religion just believe that they're right, and that others are at best wrong, and at worst working for demons and other evil entities. I have monotheistic religions in my world, animist nature-worship religions, Greco-Romanesque polytheistic religions, and a few other weird things (like the dreamborn offspring of a psionic dragon worship themselves and view the dragon as part of the world they have created).
When the existence of gods is not provable to everyone (and when I let anyone learn healing magic, including wizards and sorcerers), religions keep their role as influencing people's daily lives and values, but they don't hold sway over life and death. That midwife in your village might be a skilled expert, or might be a sorceress with a little healing magic and a few good luck charms.
I set up my world so that spellcasters tend to congregate together, ranging from small guilds that might hire out their services to cities and nations, to huge academies that hold great political power, like nations unto themselves. Mages are powerful indeed, but among humans, the ratio of normal person to spellcaster is 187 to 1 (among Elves it's more like 11 to 1), and most of them just dabble and learn a few things to make their life more interesting or comfortable.
The large groups of spellcasters try not to get involved in warfare or other political conflicts, on the whole. They prefer to keep to themselves, and though a lot of mages might volunteer to help out their home nation out of loyalty, the guild/school/organization will keep its hands clean so nobody decides to go attack them.
Most nations, however, do have a few powerful wizards working for them. Kequalak has a tradition of magical inquisitors who root out rebels and insurrectionists, and who are trained in antimagic; Tennas uses mages to perform rituals that clear the harbors of the ice that has been drifting further south these past few decades; and Nozama has a strong treaty with one magical academy that allows it to hire spellcasting mercenaries for its army.
Then you have the nifty magical creations. Sure, a teleportation circle is a great way to let messengers travel quickly from city to city, but most rulers prefer to take the extra day or two, rather than give their enemies the ability to teleport directly into their heartlands by using their own magical devices. A lot of powerful magic like this used to be more common in centuries past, but the havoc that was caused by them has made them taboo today. There used to be a huge army that could teleport wherever it wanted, and it conquered the world. After they were defeated, they magic was sealed away, and most people consider using teleportation to be like summoning demons.
There's also a lot of mistrust because of all the nasty monsters created by ancient wizards to use in their warfare. Sure, the Orb of Many Flaming Eyes sounds like an excellent guardian when you create it and can control it, but a few centuries later it's just a monster, and people curse the names of their creators.
I suppose my world is sort of a post-nuclear war world, which has recovered into a cold war state of affairs. Everyone already used all the big guns, and then they realized that, Hey, these things almost got us all killed. We have to have them, so that our enemies don't try to use theirs on us, but we'd really prefer to never have to use them.
But yes, you do still have adventurers, those people who face such great dangers that, if they survive, they have learned to do things ordinary people would think impossible. They're not controlled by nations, and they've discovered that, when fighting diabolical plans or stopping evil overlords, proper usage of such powerful magic is very effective. Once adventurers start getting powerful enough that their myths begin to spread, nations try to either get rid of them, or garner their alleigance, since it's not smart to let these folks run around with the powers they have.
Rich merchants and minor nobles tend to be the people who make greatest use of powerful magic. Merchants don't have qualms with hiring a mage now and then to get a shipment where it needs to be urgently with a teleport, and it's much easier to fit a few powerful individuals on a boat or in a caravan than it is to hire a small army of mercenaries to defend you from monsters or other dangers of the road.
Nobles, on the other hand, think of adventurers the same way that Renaissance nobility on earth thought of painters and sculptors. They provide patronage to promising heroes, hoping their heroes will become famous and gain them a positive reputation. Since the nobles are loyal to the rulers (at least in a lip-service fashion), and the adventurers are loyal to the nobles, this keeps the adventurers from going out on their own and causing trouble. One great thing about having an ancient past full of powerful magic long forgotten is that there are tons of old ruins to plunder, and sometimes all that power lying forgotten gets twisted to evil intentions. It's a perfect chance for some well-funded heroes to go and kick some ancient evil's butt, then come back and cheer the news.
Hmm, okay, now I have a different analogy. You know how much money gets spent on Hollywood movies? Okay, that money equals magical power. In some worlds, without a 'Hollywood,' that money might not even exist, because successful endeavors earn more money which can be used for greater and greater movies. A studio could easily spend its money to buy tanks and missiles and nuclear weapons, but why would they want to do that?
Similarly, powerful magic is sometimes used for political reasons, but usually it's handled so that adventurers provide entertainment for the masses. I mean, of course there are still real, legitimate bad guys to fight, but as long as magical power is being used to fight other magical power, the common person doesn't have to worry. They can just sit back and enjoy the stories of these great heroes.
Oh, and lest I forget, divination spells do cause a 'problem.' So there's a fine tradition of mages being hired to provide anti-divinatory protection to armies, nobles, and even single stores. Similarly, however, divinations let people figure out answers to simple problems:
"Why is everyone dying of this plague?"
The rats living in the filth in the streets carry the plague.
"Oh, okay. So lets keep the rats out of the town and clear out the filth in the streets."
So most of my major cities have sewers, and magic is used in other similar ways to keep things clean, like purifying water for drinking. I don't have golems performing in construction projects, and I don't have magically-lit streets, but minor magic is common, and that helps make my fantasy setting less gritty, so I don't have to worry about PCs dying of pneumonia.
