Holy Immortality, Batman!
Consider, for starters, the Cleric. Even a low-level cleric can cure diseases, heal every wound the average person receives, and purify food and water. Suddenly, the infant mortality rate drops like a rock, the population explodes, and the fuedal system breaks down.
And what about a mid- to high-level cleric? I don't have my books in front of me, but I seem to remember that somewhere in the 6th - 10th range, clerics can raise the dead. Raise the dead? Dang, there goes all fear of mortality out the window!
"Oh no, the King's been assassinated!"
"Lucky thing for us the Cardinal can resurrect him."
How do you make an exciting story in a milieu like that?
Magic Is the Crowbar That Smashes All Puzzle Boxes
Someone been murdered? Resurrection not an option? That's okay, you can still speak with dead to find out whodunnit. The Maltese Falcon gone missing? Do a divination to find out where it went. In such a context, the only thing you can do is counter magic with more magic; eventually it comes down to who's got a bigger wand, if you catch my meaning. Deduction, problem solving, etc. are all for those poor muggles to deal with.
Where's the Beef?
My D&D game doesn't run by the official numbers; according to the formulae laid down in the rulebooks, the characters have received nowhere near the treasure they should have by now, particularly in terms of magic items. So far, the nicest magic weapon in the group is a +1 ghost touch dwarven waraxe, but the characters are generally in the 6th - 7th level range, and generally fighting packs of CR 5 - 10 monsters.
But even as underpowered as they are, they are still kicking butt. I can only imagine the yawns I'd be receiving if the characters had +2 weapons, access to a boatload of potions, and rings of resistance or gauntlets of ogre power before wading into the packs of displacer beasts, fighting off the 7th-level wizards backed up by a squad of drow archers, and so forth.
The basic problem is that the rules of the D&D world don't match the behavior of the people in it. If magic exists and is so easy to get ahold of, human behavior dictates that the society must change to reflect that. Why would a peasant toil away his whole life, scraping by on one gold piece a week, when all he has to do is get a handful of guys together, head down to the ol' goblin hole, and survive an encounter or two in order to have a year's salary? Even if you assume that the average peasant is too scared to try such a thing, the risk-to-reward ratio is so out of whack that more are going to than not.
Oh well, it's a fun way to blow a few hours every weekend. :)