Debate: High Magic vs. Low

I know we all have our preferences as to whether you play a high magic world verse a low magic one. What I'm looking for is to know which one you prefer and WHY?

Feel free to extend the line of thinking to any genre: ex; is your space game rough/gritty (aliens) or of the smooth/technology-as-solved-most-problems variety.
I feel that as a flavor for a setting, it's ok for the world to be high magic. However, there are times when that gets in the way of mechanics and makes things that should be special feel mundane. When I can go into any shop in town and buy a magic sword or potion, then it makes the stuff you find in the dungeon less meaningful or useful.

For example, when I was playing in a high magic campaign years ago, my character found a magic item that allowed him to disguise himself with an illusion. He tried to use it sneak into a city where he was wanted by the local authorities. Because it was a high magic setting, the authorities had ready access to devices that see through illusions, which they routinely used at the city gates. This effectively made that magic item worthless. (or at least seem to be. There could certainly be situations where it would come in handy, but those never came up.)
Agreed. There's a gm/player relationship when it comes to certain magic items that is always on a precarious balance.

Players generally want the items they get to 1) work and 2) be able to use it in inventive ways. Often looking for credit/xtra exp for doing so.

Gm's give items out has rewards, and generally, are good with any item that doesn't allow players to 1) circumnavigate their adventures 2) blow up their world, 3) be too over powered for their level/cr/circumstance.

In 3.5 you could get a Cloak and Boots of elvenkind, each a +5 (or +4?) bonus to hide, if a character can get that early enough they can use that to supreme advantage and that's not even high magic... I've found that, unfortunately, to run a good high-magic campaign requires a certain trust between player/gm: that the one won't render the players skills/items useless and the player won't go munchkin on the gm.
My tastes vary depending on the world. Even in my low magic games , though (where buying and selling magic items is unheard of), I ask the players to give me a list of the sorts of items their characters would like. I then tailor treasure drops to include some or all of those, along with randomly generated items. (At least, that is, in D&D 3.5 where magic items are part and parcel of the mechanics of character design.)

Low magic games are darker and grittier in general at lower levels, but I tend to find that the party will have multiple spellcasters anyway...which counts greatly in their favor at higher levels ultimately turns the low magic environment to their advantage.

High magic games do have a tendency to go off the rails more than low magic ones, in my experience, so it helps to have players that are cooperative enough not to break the game.
Using DnD or Pathfinder as a point of reference:

Low magic can be a lot of fun for the point that when your players get a magic item, it makes it that more cherished. However, this comes with the responsibility that the GM understand the limitation of low magic on a party. Especially in the late game, there are many monsters that require sufficiently strong magic to overcome. Higher end devils for example need both magic and holy weapons to beat their DR. Obviously brute strength can defeat this, but it makes for a tougher fight.

The other off shoot of that is the difference between fighter types and caster types. Unless the caster abilities are dumbed down to go with the limited supply of magical items, it can give them an unfair advantage over fighter types. This too however would need to be handled by a careful hand as hobbling a magic user too much could lead to your players not being interested in playing those types.

Then what about characters that have their natural abilities boosted without the use of magic, such as a monk for example. Do you reduce down their abilities too?

There are a lot of things to consider, and like the other mentions, I would also agree that it comes down to the feel that BOTH the players and the GM want. It is important that there is a consensus on which way the road will go.
The efforts I've both seen and made to nerf casters in response to low magic campaigns were all "troubled" to say the least. Nerfing any class breaches player expectations and is a hard sell. Enhancing the combat classes at high levels is the better option.

If you just "have to" take power from casters, then the rule I've used that was the least troubling was to require multiclassing such that every over level was from a non-casting class (or at least a different casting class). As you suggest, though, that drove some folks away from caster classes entirely.

I do agree that monster selection in low magic games is key. A devil can be a major enemy, but it's not really low magic if they are overused. (Low-magic for thee, but not for me would be a tough game for players to survive.)

Edit: I should add that in the Nehwon/Lankhmar games they also had a rule that "Black magic" practitioners (arcane casters) developed deformities of increasing severity as they grew more powerful. That was flavorful and tended to limit players from taking at least arcane casters to high level.
My 2¢:
Just because you're running a low magic campaign doesn't mean that the PCs need to be low magic. At high levels, spell casters would have access to abilities that most NPCs would consider 'god like'. This could provide lots of role play opportunities as the PCs would be feared. Some towns would shun them, fearful of the destruction they could cause. Others would treat them like royalty or gods, believing that they can protect them, grant wishes, or make them rich (You can cast Fireball? Then surely you can change all this lead into gold, right?).

This reminds me of "The Slayers" anime series. While not totally a 'low magic' setting, the main characters were, by a wide margin, the most powerful people in the world. This made them both feared and highly sought after.
I generally run my games where the Age of Magic is long past. While the stuff you can buy in town is neat they are limited items. The item has so many charges or can only be used so many times per day and uses mana. Where as items from the old days have a soul or spirit locked inside granting you the powers they have. You just have to be on their good side.

If running high magic I generally do as above and make it that you can see an item being made that can gruesome and make players rethink wanting magical Items.

I do not run "romantic" settings ever I tend to run gritty and often horrific games. This also helps to curve those who tend to be I HAVE ALL THE POWER and go crazy with magic items/spells.
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