ETAOIN SHRDLU golf

Python 2 or 3 - 77 75 bytes

f=lambda s:''.join(sorted(map(chr,range(65,91)),key=s.upper().count))[::-1]

I had an answer before that grabbed input from STDIN, but I realized it was technically invalid. I used input() which gets only a single line, but the question's example input implies that it should handle multiple lines at once. To meet spec, I turned my answer into a function that takes a string argument. To my surprise, it was two bytes smaller! It didn't occur to me that print(...) and input() were longer than f=lambda s: and s.

This also makes the answer compatible with both Python 2 and Python 3. Originally it was only Python 3, because it used input() (which was called raw_input() in 2). Now that it's a function, it works in both.

Explained

                                  range(65,91)                              # The numbers 65 to 90
                          map(chr,range(65,91))                             # Convert to ASCII

                                                    s                       # The input string
                                                    s.upper()               # Convert to uppercase
                                                    s.upper().count         # Function literal for 'how many times the argument appears in the string'

                   sorted(map(chr,range(65,91)),key=s.upper().count)        # Sort by that function
           ''.join(sorted(map(chr,range(65,91)),key=s.upper().count))       # Concatenate to string
           ''.join(sorted(map(chr,range(65,91)),key=s.upper().count))[::-1] # Step through by -1 (i.e. reverse string)

  lambda s:''.join(sorted(map(chr,range(65,91)),key=s.upper().count))[::-1] # Make it a function (`return` is implicit for lambdas)
f=lambda s:''.join(sorted(map(chr,range(65,91)),key=s.upper().count))[::-1] # Give it a name

CJam, 21 19 bytes

qeu:A;'[,65>{A\-,}$

Try it online.

Example

$ cjam etaoin.cjam <<< "~XyxY YyxZ"
YXZABCDEFGHIJKLMNOPQRSTUVW

(no newline)

How it works

qeu:A; " Read from STDIN, convert to uppercase, save in the variable “A” and discard, ";
'[,    " Push an array of all ASCII characters before “[” (NUL to “Z”).               ";
65>    " Remove the first 64 characters (NUL to “@”).                                 ";
{      " Sort the array of characters by the following mapping:                       ";
  A\   " Swap the character with the string saved in variable “A”.                    ";
  -    " Remove all occurrences of the character from the string.                     ";
  ,    " Push the length of the string.                                               ";
}$     "                                                                              ";

More occurrences means more characters get removed, so the most frequent characters appear at the beginning of the array.

Bash, 65 bytes

(tr a-z A-Z;echo {A..Z})|fold -1|sort|uniq -c|sort -nr|tr -dc A-Z

Example

$ bash etaoin.sh <<< "~AbaB BbaC"
BACZYXWVUTSRQPONMLKJIHGFED

How it works

(              #
  tr a-z A-Z   # Turn lowercase into uppercase letters.
  echo {A..Z}  # Print all uppercase letters.
) |            #
fold -1 |      # Split into lines of length 1.
sort |         # Sort those lines (required for piping to uniq).
uniq -c |      # Print the frequencies of all lines.
sort -nr |     # Sort by frequency (reversed).
tr -dc A-Z     # Remove everything that's not an uppercase letter.