Some of the 'artificial' sweeteners have been formulated to be heat-stable or similar for baking; check the packages.
Sugar alcohols are less likely to leave an aftertaste.
In baking -- cakes and such -- you need to know what sugar is *doing* ... sometimes it's just sweetness, sometimes it's a matter of mixing with oil or eggs and aiding with moisture. In a lot of mousse and pudding type things you can *reduce* sugar and get used to a less-sweet produce. In ice cream, though, if the sugar content is too low you'll get a hard product.
In baking, rather than entirely replacing sugar, I'd first substitute for other kinds of sugar. Find recipes that use unsweetened applesauce; applesauce is often used as an oil or egg replacement in vegan baking and helps with moisture. Also, some spices like cinnamon and mint serve as 'sweetness replacers'. But as another poster commented, if you want to eliminate sugar, you may have to give up a lot of sweet baked goods ... sugar isn't just for sweetness there, it's often an integral component to texture and such. Check also: some of the diabetic cookbooks.
Best of luck.
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