I'm thinking of removing magical weapons and armour completely from my campaign setting and from my random charts and so on. This would have a number of effects.
The most obvious effect would be that magically overpowered characters would be a lot rarer. Characters that are powerful would be so through their innate abilities, or other means such as politically. This would make strongholds more desirable goals for high level characters.
The second effect is to de-emphasise combat and make players think on their feet a bit more. Facing off against a dragon is much tougher with a normal sword than a +5 sword of dragon annihilation. Players would have to be very inventive about dangerous combat situations and may even avoid them.
The third effect is that plot-centric special items would be incredibly special. Instead of their being a mass of +2 swords lying around, there could be one Excalibur that adventures and the plot would flow around. Who wields this mythical blade has serious significance. Perhaps only the gods can craft these items and it is beyond the ken of all mortal men, although the knowledge is sought after with a passion.
The fourth effect is that magical items would be highly sought after instead. Suddenly, by way of example, finding a flying carpet is a massive deal to even high level adventurers. Of course, I would need a very large assortment of magical miscellanea to stop the same lot from repeating over and over, but that would be quite fun to come up with, I think, especially if the items are not directly combat or stat bonus related. It could add a lot of spice to what might otherwise another run of the mill campaign.
What's even better is that I could probably get away with it. All the player characters are currently either first or second level and so do not currently own anything magical anyway, the adventures that they have been on so far have not uncovered any. Valuable trinkets, yes, but so far, nothing magical.