The question underneath "should I replace it"

An old appliance rarely stops working outright; it just gets more expensive to run every year it ages past its efficiency baseline. The number that actually answers "is it worth replacing" is the yearly running-cost gap between what you have and a current certified model, multiplied by however many years you'd keep the new one, compared against what the new one costs to buy.

A worked example

Take the ABL AREF18**, a current certified refrigerator at $68/year to run. If an older, uncertified fridge in the same size class runs closer to the pre-ENERGY-STAR baseline (routinely 40 to 50% higher energy use for units from the 2000s or earlier, per EPA's own certification history), the running-cost gap alone can be $30 to $47 a year. Over a 13-year refrigerator lifespan, per NAHB, that's real money before counting anything else.

When the math doesn't favor replacing

If your current appliance is already reasonably efficient, or nearing the end of its life anyway, or the category has a low absolute running cost to begin with (a washing machine averages well under $20/year to run; the gap between an old and new one is real but small in dollar terms compared to a refrigerator or water heater), the purchase price of a new unit can outweigh years of savings. This site's per-model pages show both the running cost and the category's typical range, so that comparison uses your actual numbers rather than a rule of thumb.

Where the biggest gaps actually are

Water heaters and refrigerators run the highest absolute annual cost of the eight categories here, so a percentage difference in efficiency is worth the most in real dollars for those two. See any water heater or refrigerator page for the specific spread, or the methodology guide for how every figure here is sourced.