Tell them. I would recommend going through scenarios with them. Everyone thinks of the persistent vegetative state, but it's very unlikely you'll end up in one. It's more likely you'll be days away from death and passed out in a haze of exhaustion and morphine, with a ventilator doing little more than prolonging this scenario. Do you want the ventilator removed? Do you want CPR if you're hospitalized for a terminal condition? What if you're hospitalized for a non-terminal condition?
> Is it sufficient enough to have a living will, for example?
It sure helps, so do that. But also make sure to designate one of your loved ones in particular as your power of attorney. Make sure it's someone who understands and is capable of carrying out your wishes. That person will stay in close contact with health care professionals and has the legal right to make any and all decisions should you be incapacitated. In my limited experience, no one even looks at the living will if there's someone with clear power of attorney telling them what to do.
This person has an even more important job, at least in the American health care system: they're often the only one who talks to all the doctors and has the big picture. If you're seeing five different specialists, and they're all talking about their own specialties, no one is necessarily in charge of the big picture. In the outpatient world you have a primary care doctor, but when you're hospitalized, this guy's out of the picture. There is probably a hospitalist in charge of your care, but just like the nurses, the hospitalists rotate on shifts, and don't really coordinate with specialists so much as just trying to keep you alive. You need someone to be power of attorney, and to take the job seriously. One of the striking things, to me, about Steve Jobs' biography was that even for him, this was true--his wife was the one coordinating the doctors and keeping in charge of the big picture.
> Are there documents out there that I should be carrying in my wallet, and do paramedics seek these documents out in an emergency?
No. I've had paramedics at my house for my dad twice, and they never looked in his wallet. On the other hand, I was there both times.
The job of a paramedic is to stabilize you, gather whatever information they can, and take you to the ER. They probably don't give a shit about your wallet or your cell phone. Whatever procedure there is for identifying someone's next of kin and finding their advance directives, it's done in the hospital. Most of the time they just ask you, if you're conscious, and they ask whoever is physically with you at the time. They would only resort to searching you and your effects if you were completely alone, or if no one around you knew anything or anyone. So designate your power of attorney and designate that person as your emergency contact at work. If you don't live with that person, make sure a neighbor or roommate or someone else you live with or close to has that person's number programmed into their phone and knows to contact them. You want a person you trust, not just a tattoo or bracelet or document, in charge here.