For the substitutions below, I relied heavily on an old cookbook I have, Entertaining Without Alcohol, by Dorothy Crouch.
Almond Extract
Replace some of the flour with an equal amount of ground almonds, or replace some of the shortening/oil with the same amount of marzipan. The dish will be a little grainy.
Brandy
“Burnt” sugar (caramel) syrup: melt sugar until dark golden. The darker it gets, the less sweet it will be; too dark will be bitter. Add an equal amount of water, stirring in drop by drop as it will splatter. A little goes a long way; use 1 Tbsp. or less.
Calvados or Applejack
Apple cider (fresh, if you can get it). The dish will taste sweet if you use more than ¼ cup of this.
Cassis
Blackberry juice, or add water to blackberry preserves/jam/syrup. Black currant or elderberry may be used instead. If you have the fresh fruit, cook and press it through a sieve if you like.
Cognac
Apple cider with 1 Tbsp. dark brown sugar per ½ cup of cider
Reduce sugar in the recipe
Curacao, Grand Marnier, or Cointreau
Frozen orange juice concentrate, or tangerine juice. For Curacao, also add 1 tsp. grated orange zest (or a little orange oil or extract) per ¼ c. concentrate
Framboise
Replace with an equal amount of unsweetened raspberry juice, or add water to raspberry jam to make it the consistency of juice. If you don’t have any, orange is usually a complementary flavor, or a little almond.
Lemon Extract
Same as Orange Extract, but use lemons. Use a light hand; too much oil and peel make a dish bitter. Use ¼ tsp. of zest or ¼ tsp. dried peel for ¼ tsp. of extract.
Orange Extract
The oil you get from bending an orange peel over a dish, plus 1 Tbsp. grated orange zest. Or use 1 Tbsp. dried orange peel.
Red Wine
Beef broth, tomato juice, and/or vegetable juice (like V-8). Don’t substitute cream of tomato soup; it’s too sweet.
Reduce salt by ¼- ½ tsp. for each cup of broth used.
Rum, Light
Simple syrup made using light brown or granulated sugar
Reduce sugar in the recipe
Rum, Dark
Simple syrup made using dark brown sugar
Reduce sugar in the recipe
Sherry
Replace 1 Tbsp. of butter or oil with 1 Tbsp. walnut oil, or add a couple tablespoons finely chopped walnuts.
Vanilla Extract
Use vanilla sugar, vanilla syrup, or vanilla ice cubes. See under this chart for instructions.
White Wine
Replace with an equal amount of chicken broth, fish stock, or clam juice. If you don’t need much flavor, use water or a little apple cider vinegar mixed with broth.
Reduce salt by ¼- ½ tsp. for each cup of broth used.
Wine Vinegars
My understanding of wine vinegars is that there is no alcohol remaining; all vinegar goes through a fermenting stage first. Specific strains of bacteria are added to this, and they digest the alcohols, leaving acetic acid as a byproduct. "White wine vinegar", then, means that at one point the liquid was white wine, before the bacteria changed it. You could just call it "white grape vinegar"; that's what it means. If anyone knows different than this, please let me know. If you're still concerned with using them, here are some substitutions: White wine vinegar: use distilled white vinegar. For red wine vinegar, use cider vinegar or some other made from fruit (raspberry, pomegranate, etc.)
Vanilla Cubes: Chop 2-4 vanilla beans and add 1 quart (4 cups) of water. Bring to a boil; simmer until reduced by half, to get 2 cups. Cover and let sit overnight to intensify. Pour through a fine-mesh sieve or cheesecloth, pressing on the bean bits to get as much flavor out as you can. Pour this liquid into ice cube trays; it will be enough for two trays. When frozen, transfer cubes to freezer bags. Remember to label them!
Vanilla Sugar: Cut 2 vanilla beans into 1” pieces. Stir them into a container with up to five pounds of sugar. Let this sit for a week or more (longer= better flavor). To use the sugar, pour it through a sieve. Alternately, you could very finely chop those vanilla beans, and use the sugar with flecks in it.
Vanilla Syrup: Follow instructions for Vanilla Cubes, above, except: instead of straining and freezing the water into cubes, mix the liquid with the bean bits in a saucepan with 2 cups of sugar. Bring to a boil, cover the pot for a few minutes to let any stray sugar crystals dissolve in the steam. Cool and pour into a jar, including the bean bits. If the mixture crystallizes, reheat it to dissolve. Reduce sugar in the recipe by about the same amount of syrup used.