I love my Hardcore characters and the rule set of the game from that time. However, the permadeath just became too discouraging, and I found I didn’t log in because I didn’t want my characters to die. As it turns out, you can always transfer them from the Death Realm to a Classic Era Realm where they can live their lives, and when misadventure strikes, it’s ok. You don’t lose everything. I personally lost 6 characters and immediately deleted them. My husband lost approaching 30 characters, oops.
I thought at first you could only transfer your Dead character, so I sent my main Hardcore character to die by murlocs.

When you die it will say try again and bring you to the character select screen.

The steps for moving a lively character and a dead character are the same.
From the character Select Screen pick your character.

In the lower left, click on Shop.
Click on Free Character Transfer and Buy Now

Your current realm is displayed, and the drop down option to choose a character to be transferred.

Select Character and a drop down list will appear. Pick your character here.

Now you have the option to select a Classic Era Realm (not Cataclysm Classic, just the Era Servers using the same rule sets as Hardcore.)

Verify your selection, and on the Character Select Screen you will see a Gear by the character whose transfer you requested.

A bit of trouble with Serine! When I looked back at her she had an odd code by her name. When I hit Enter World, I got this notification that her name was taken on the new server. Typed in a new name and there we go.

My first transfer was an intentionally dead character. The second was my Banker (not dead). For a moment when I tried to log my Banker in it said Character Not Found (small panic), but I hit Enter World again and voila!
The items in your Inventory and Bank transfer with you.

Classic Era servers you can transfer to Free from Hardcore:
Arugal PvP
Atiesh PvE
Benediction PvP
Bloodsail Buccaneers RP
Faerlina PvP
Grobbulus PvP
Mankrik PvE
Sulfuras PvP
Whitemane PvP