Common ingredient substitutions for 1 cup of:

replace half the amount of butter with pureed fruit

2/3C plain yogurt + 1/3C milk OR
1T white vinegar or lemon juice + 1C milk, let stand for 10-15 min

1 large egg = 2 ounces = 1/4 C
for one egg used as a binder:
2T freshly, finely ground flax seed (previously ground seeds go rancid) + 3T warm water OR
1T unflavored gelatin + 3T warm water OR
1T cornflour + 3T water OR
2T water + 2T flour + 1/2T shortening + 1/2t baking powder OR
1/4C pureed tofu OR
1/4C pureed fruit OR
1/4C mayonnaise
for 2-3 eggs used as a leavener:
1T baking powder + 1T oil + 1T warm water per egg OR
1T baking powder + 1T vinegar + 1T warm water per egg

Mascarpone Cheese
mix together 6oz cream cheese, 2T heavy cream and 1 1/2T sour cream

1/4 C silken tofu + 3/4 C water + pinch salt, blended til smooth
1 cup water plus 1 1/2 tsp butter (in baking)
Soy, rice, or other milk substitute with varying changes to flavour

Milk, evaporated or sweetened condensed
I have had success using the same volume of plain milk in pumpkin pies with no significant loss of firmness. Sweetened milk contains 60% sugar, so be aware of the reduction in sweetness when substituting.