I have AHS and have used it a few times over the years.
It is about $50 a month, so about $600 a year for the service.
When you call for service, they will charge you a $75 service fee.
I've had my service for around 5 years, so I paid them about 3k, plus the service fees everytime they come out.
I've gotten a check for $684 for a washer that could not be repaired and $586 for a dryer that could not be repaired. I also got around $1100 for a water heater replacement and installation. I did have to pay $225 for these services.
Additionally, I've had them unclog my bathroom shower drain, kitchen drain, and main line over the years. Again they charge $75 per visit.
Over the last 5 years they are still up money wise, but eventually when my AC, cooktop, or oven goes out I will be in the money.
My sister has Viking appliances and was recently paid $6800 for a refrigerator they could not repair. She has been paid out for a washer, dryer, water heater, and dishwasher. Not sure what they paid out for those.
I believe if you have higher end appliances AHS is worth it. My washer and dryer were given to me. They were probably the cheapest Kenmore washer and dryer at the time and probably 20-25 years old, so I was ok getting around $1300 to replace them.
Oh, and they try to do everything they can to repair the appliance before paying you out.