I have a cake that calls for 4 Tablespoons of brandy. I don't have any brandy in the house, nor any kind of liquor at all (besides maybe red wine vinegar which doesn't help much). Is there anything I can substitute, or should I just skip? (I think I've skipped the brandy sometimes before when making this recipe and it came out fine.)
I would probably make a simple syrup and heat it and then steep some chopped raisins or dates in it for an hour or two, and then use some liquid from that instead of the brandy. That way you're adding some flavor, but without the alcohol. Much like the other suggestions, it won't be exactly the same as adding brandy or other liquor, though.
I don't think there is a recipe that will give you trouble if you just skip the liquor.
As for substitutes, I would says add a bit of brandy extract, you can find small bottles in the supermarket. You can add other liquor extracts (rum etc.) if you don't like the taste of brandy. But be careful to adjust the amount. I think 1 Tbsp of extract will me more than enough in your recipe here.
I don't wish to detract from those saying "skip it", except that I would draw attention to the fact that if you choose to "skip it" there is a price to pay, you loose the flavor that brandy provides. This does not mean that your product will be 'bad' just 'different'.
As for those advancing the idea of Vanilla, In the US Vanilla Extract is a MINIMUM of 35% alcohol (or 70 proof). The flavor change may indeed be fine, but it is not an alcohol free decision to switch from brandy to vanilla extract.
The actual process of baking removes much (but not all) of the alcohol from the final product. Then there is apportionment to consider. 4 Tbl is 2 shots, or roughly the amount of alcohol in 2 beers, before reduction. If you start with 4 Tbl and bake for one hour you are down to 1/2 of one beer, apportioned over 8 to 10 servings. Each consumer will receive the approximate amount of alcohol as the consumption from looking at a bottle of beer (ok, 1/16 of a beer...)
Now I appreciate that you may well have important reasons to maintain a standard of "no alcohol" and I would not attempt to dissuade you from those values. If, however, something like vanilla extract is an acceptable cooking ingredient then too should small amounts of other alcohols be acceptable when treated as an ingredient.
That said, if you wish to substitute for brandy then your best choice is whiskey.
Brandy is a distilled wine (fermented grape mash) which has been aged in oak barrels. Whiskey is distilled from a fermented grain mash and then aged in oak barrels. In each case the oak is the primary source of flavor (while distillation and quality of the mash contribute to the 'smoothness' the flavor is OAK)
Depending on the recipe, you might be able to substitute additional vanilla extract to give more flavor. I wouldn't recommend doing a whole 4 tablespoons as vanilla is much more concentrated than actual brandy, but maybe 1-2 teaspoons vanilla + some water or apple juice to end up with the right overall amount of liquid? If cake recipe uses milk already, use vanilla + milk.
I have made this substitution successfully with something that's similar to the current answers, but gives a richer taste.
The best, but time-consuming option
Make a small amount of caramel*, maybe a single tablespoon per 100 ml of brandy-to-replace. You'll have to use a small vessel, maybe a muffin cup, if that little sugar is spread in a normal-sized pot, it will go from pale to burning almost instantly. When it caramelizes, add clear apple juice in the needed amount, take from the heat, and wait until it is properly dissolved. When it cools down a bit, add some drops artificial brandy flavoring (check if it is alcohol free if that's a concern for you) and then top up to replace the juice that evaporated when hitting the hot caramel.
The easier option with less complex flavor
Add brandy essence to apple juice.
This also works for other alcohol types such as rum, if you have the proper essence. Also, many recipes are very tolerant to having the alcohol type "replaced", for example I have used this technique with rum essence in a recipe which called for brandy.
* Here I mean to caramelize sugar without adding butter or dairy - I know people do that, but in my terminology the result would be called caramel sauce, toffee, or something else. When I say caramel, I mean sugar heated until it's brown.