Decreasing the sugar amount by 1/3 to 1/2 does not usually affect the recipe's chemistry too much, although the texture can sometimes be a bit different (for example, brownies will be cakier and less fudge-like).

There's a natural sweetener called Stevia, which a lot of people use and swear by, but it does have a bit of an aftertaste and I'm not sure how it would affect the chemistry of baked items, as it's a very concentrated powder and you need to use a very small amount to get the same sweetness as sugar. There is also a product on the market called Sweet One, which can be used in place of sugar in baked as well as non-baked items. As far as we know, it's just fine for diabetics.