Using the Terminal keybindings with bash on macOS

Mac OS X's terminal is BASH, here's some BASH shortcuts:

Ctrl + A    Go to the beginning of the line you are currently typing on
Ctrl + E    Go to the end of the line you are currently typing on
Ctrl + L    Clears the Screen, similar to the clear command
Ctrl + U    Clears the line before the cursor position. If you are at the end of the line, clears the entire line.
Ctrl + H    Same as backspace
Ctrl + R    Let’s you search through previously used commands
Ctrl + C    Kill whatever you are running
Ctrl + D    Exit the current shell
Ctrl + Z    Puts whatever you are running into a suspended background process. fg restores it.
Ctrl + W    Delete the word before the cursor
Ctrl + K    Clear the line after the cursor
Ctrl + T    Swap the last two characters before the cursor
Esc + T  Swap the last two words before the cursor
Alt + F  Move cursor forward one word on the current line
Alt + B  Move cursor backward one word on the current line
Tab      Auto-complete files and folder names

The one you are looking for is Ctrl + H. (This is the same as hitting the backspace key)

If you are looking for an escape character to go back one character, you are looking for \b. As in:

$ echo -e "one two\b\b\b\b three" # Will echo "one three"

One way to deal with 'meta' key sequences not working on the OS X terminal is to assign specific character sequences to particular keypresses. For those of us with non-US keyboards, this is often a better solution than the "Use option as meta" setting mentioned in the comments of other answers. (Many international Mac keyboards are essentially unusable for development work without the Option/alt key because certain critical characters are otherwise unavailable. There's no # on a UK Mac keyboard, for example.)

To get word-left and word-right working for bash, I've used the "Keyboard" section of the Settings in Terminal. You can tell it to generate particular code sequences when particular keypresses are made. I've got mine configured so that alt+◀ generates \033b (that's actually two characters: Esc, and then a lowercase b) and alt+▶ generates \033f (i.e., Esc f). This lets you use the arrow keys with the option key held down to get the word left and right behaviour.

What I've not yet worked out is how to get the Esc key to work - in theory you should be able to use that for 'meta' sequences but it appears not to work. (So just typing Esc+b should go back one word.)

If you have a US keyboard layout, or some other keyboard in which Apple have seen fit to provide all the keys you actually need, then as others have suggested, "Use option as meta key" (also on the Keyboard section of Terminal's settings) is probably a better choice because you'll be able to get to any meta key combination. With that switched on, Alt+b works as expected.

On my UK mac, ALT + cursor left/right goes back/forward one word. Absolutely essential.