Mayonnaise
Mayonnaise is maybe the most contentious condiment. Whatever your opinions are about the egg-based spread, you can't deny its culinary flexibility. Mayonnaise works well in cakes because the oil keeps the crumb moist while the acidic flavor balances out the sweetness of the batter. According to the Chobani Kitchen Conversion Chart (via KosherEye), you can use a 1-to-1 ratio of mayonnaise to Greek yogurt in baked products.
Mayonnaise is somewhat richer than Greek yogurt, so if you want to use Greek yogurt instead of mayonnaise in a tuna salad, add a few teaspoons of oil to equal parts Greek yogurt. To enhance the flavor and texture of Greek yogurt, blend it with white vinegar and cornstarch. If you haven't already guessed, there are some instances where replacing mayonnaise with Greek yogurt is just not an option. Unless you have the ability to consume a dish of mayonnaise without gagging.