If you're ready for a Facebook break, you have two options: deactivate or delete.
This option couldn't be easier. On the desktop, click the drop-down menu at the top-right of your screen and select Settings. Click Security on the left, and you'll see a "Deactivate My Account" link at the bottom. If you're on your mobile device, such as using Facebook for iOS, similarly go to Settings > Account Settings >Security and you'll see a link that says "Account – Deactivate."
Facebook doesn't take this lightly—it'll do whatever it can to keep you around, including emotional blackmail about how much your friends will miss you.
As such, "Deactivation" is not the same as leaving Facebook. Yes, your timeline will disappear, you won't have access to the site or your account via mobile apps, friends can't post or contact you, and you'll lose access to all those third-party services that use (or require) Facebook for login. But Facebook does not delete the account. Why? So you can reactivate it later.
Just in case that expected re-activation isn't in your future, you should download a copy of all your data on Facebook—posts, photos, videos, chats, etc.—from the settings menu (under "General").
To fully delete your Facebook account forever and ever, go to the Delete My Account page at facebook.com/help/delete_account. Just be aware that, per the Facebook data use policy, "after you remove information from your profile or delete your account, copies of that information may remain viewable elsewhere to the extent it has been shared with others, it was otherwise distributed pursuant to your privacy settings, or it was copied or stored by other users."
Translation: if you wrote a comment on a friend's status update or photo, it will remain even after you delete your own profile. Some of your posts and pictures may hang around for as long as 90 days after deletion, as well, though just on Facebook servers, not live on the site.
Deletion On Behalf of Others
If you want to notify Facebook about a user you know is under 13, you can report the account, you narc. If Facebook can "reasonably verify" the account is used by someone underage—Facebook bans kids under 13 to comply with federal law—it will delete the account instantly, without informing anyone.
There's a separate form to request removal of accounts for people who are medically incapacitated and thus unable to use Facebook. For this to work, the requester must prove they are the guardian of the person in question (such as by power of attorney) as well as offer an official note from a doctor or medical facility that spells out the incapacitation. Redact any info necessary to keep some privacy, such as medical account numbers, addresses, etc.
If a user has passed away, a legacy contact—a Facebook friend or relative who was designated by the account owner before they died—can get access to that person's timeline, once approved by Facebook. The legacy contact may need to provide a link to an obituary or other documentation such as a death certificate. Facebook will "memorialize" the page so the deceased timeline lives on (under control of the legacy contact, who can't post as you), or if preferred, remove it.
Designate a specific legacy contact person to handle your account after your passing. You can find that under Settings > Security > Legacy Contact. Once you set one up, you'll get a notification every year from Facebook to double check that the contact should stay the same. You can also take the extra step of making sure that after you die, if the legacy contact does report you to Facebook as deceased, your account gets deleted (even if the legacy contact wants the timeline to be memorialized).