Actually it depends on what shell you use, however most shells have similar bindings. The bindings you are referring to (e.g. Ctrl+A and Ctrl+E) are bindings you will find in many other programs and they are used for ages, BTW also work in most UI apps.
Here's a look of default bindings for Bash:
Most Important Bash Keyboard Shortcuts
Please also note that you can customize them. You need to create a file, name as you wish, I named mine .bash_key_bindings and put it into my home directory. There you can set some general bash options and you can also set key bindings. To make sure they are applied, you need to modify a file named ".bashrc" that bash reads in upon start-up (you must create it, if it does not exist) and make the following call there:
bind -f ~/.bash_key_bindings
~ means home directory in bash, as stated above, you can name the file as you like and also place it where you like as long as you feed the right path+name to bind.
Let me show you some excerpts of my .bash_key_bindings file:
set meta-flag on
set input-meta on
set output-meta on
set convert-meta off
set show-all-if-ambiguous on
set bell-style none
set print-completions-horizontally off
These just set a couple of options (e.g. disable the bell; this can be all looked up on the bash webpage).
"A": self-insert
"B": self-insert
"C": self-insert
"D": self-insert
"E": self-insert
"F": self-insert
"G": self-insert
"H": self-insert
"I": self-insert
"J": self-insert
These make sure that the characters alone just do nothing but making sure the character is "typed" (they insert themselves on the shell).
"\C-dW": kill-word
"\C-dL": kill-line
"\C-dw": backward-kill-word
"\C-dl": backward-kill-line
"\C-da": kill-line
This is quite interesting. If I hit Ctrl+D alone (I selected d for delete), nothing happens. But if I then type a lower case w, the word to the left of the cursor is deleted. If I type an upper case, however, the word to the right of the cursor is killed. Same goes for l and L regarding the whole line starting from the cursor. If I type an "a", the whole line is actually deleted (everything before and after the cursor).
I placed jumping one word forward on Ctrl+F and one word backward on Ctrl+B
"\C-f": forward-word
"\C-b": backward-word
As you can see, you can make a shortcut, that leads to an action immediately, or you can make one, that just inits a character sequence and then you have to type one (or more) characters to cause an action to take place as shown in the example further above.
So if you are not happy with the default bindings, feel free to customize them as you like. Here's a link to the bash manual for more information.