Everyone's talking about gunpowder. Would gunpowder be developed? Pursued? etc? Well, caelic said it on the last page, but didn't really emphasise it enough: there are already explosives in the game. Not only that, we have chemical (alchemical, really) mixtures that cause explosions in various different ways, including smoke, poison, and plain old fire, all in the controlled ways that a gun of some sort would require. All we need now are groups known for tinkering, and making mechanics. Something like, oh, say, gnomes (or dwarves). I know there's at least one setting where steam power is minorly available, as well, and that's not far off from what gunpowder would require. Now, again, magic is going to make it different. It makes it easier to produce mundane things, and it makes it easier to make mundane things better. And it also is a different approach to the warfare.
So what I think is that "gunpowder" weapons would and should exist in this setting (this setting being the prototypical D&D setting), it's just that they are powered by a combination of magic and alchemy, rather than chemistry. I think that the guns available would be a gnomish (dwarves tend to prefer the hammer, of course) rarity, only available from gnomes and those capable of a gnomish level of tinkering. So I'd imagine that they are available as expensive, but effective, hunting tools and murder weapons. NOt fit for an army, except for special forces. So an adventurer could definitely have a gun.
This does play into the horrible gold problem of the game. Which is another discussion entirely, but I'm thinking an economy where magic doesn't cost gold (instantaneous does (potions), and services do, but things like a +1 weapon doesn't cost gold). Guns cost a lot more than a bow, but are better. Because they cost more, they are harder to come by, and reduce your wealth for buying other things, like armor (full late costs a lot, but is better, and the same thing happens, so you generally can't have medium or heavier armor and a gun due to cost).