What can interfere with pacemakers and implantable defibrillators?

Pacemakers. Strong magnetic fields such as those used in security metal detectors and magnetic fields produced by large electric motors can interfere with pacemaker and defibrillator function. They may not necessarily turn a device "off" but can interfere with its programming. With only rare exceptions, patients with these devices need to avoid MRI scanners. Patients with these devices can have ct scans.
Not much. Common household appliances and cellular phones are generally safe to use near an implantable defibrillator. It is best to avoid sources of significant electric current. For example, you should keep your icd 2 feet from an arc welder. You should not lean over your car engine while it is running. It is best to also keep large magnets off your device as well since this can affect its performance.
High Energy Sources. Induction cooktops arc welders, esp 240v and/or >200a alternators and other high-current generators nerve stimulators microwaves, phones, etc are safe. On manufacturers advice, any radio transmitting or receiving device is supposed to be ~6+ inches from the device but i've yet to see a cellphone interfere with a modern device.
It Varies. Sources of electronic or magnetic fields (emi) can cause inappropriate function of a pacemaker or icd. Examples of these are mris, strong electric motors, or even security systems. Radiation (like for cancer therapy) can also damage or interfere with pacemakers/icds.