So, took your code out of the function and ran some tests.

import sys
buffer = []
while run:
    line = sys.stdin.readline().rstrip('\n')
    if line == 'quit':
        run = False
    else:
        buffer.append(line)

print buffer

Changes:

• Removed the 'for' loop
• Using 'readline' instead of 'readlines'
• strip'd out the '\n' after input, so all processing afterwards is much easier.

Another way:

import sys
buffer = []
while True:
    line = sys.stdin.readline().rstrip('\n')
    if line == 'quit':
        break
    else:
        buffer.append(line)
print buffer

Takes out the 'run' variable, as it is not really needed.

It's simpler:

for line in sys.stdin:
    chrCounter += len(line)

The file-like object sys.stdin is automatically iterated over line by line; if you call .readline() on it, you only read the first line (and iterate over that character-by-character); if you call read(), then you'll read the entire input into a single string and iterate over that character-by.character.

Use the fileinput module:

import fileinput

for line in fileinput.input():
    pass

fileinput will loop through all the lines in the input specified as file names given in command-line arguments, or the standard input if no arguments are provided.

Note: line will contain a trailing newline; to remove it use line.rstrip().

The solution to this problem depends on the OS you're using.
Basically, if you want multiline input, you'll have to use sys.stdin.read() instead of sys.stdin.readline(). Since sys.stdin is a file-like object in Python, the read() method will read until it reaches the end of a file. It is marked by a special character EOF (end-of-file). On different OS'es there is a different way of sending it.

On Windows:
Press Ctrl+Z after your input and then press Enter:

2 10
20 2
30 3
^Z

On a Unix-based OS:
Press Ctrl+D after your input. No Enter is required (I believe)

If you want to get a list [2, 10, 20, 2, 30, 3] from your input, you're fine. The split() method splits by whitespace (spaces, newlines, etc.).

What have you tried, and what form does the input take? If it's typed in, maybe you want something like this:

lines = []
line = input('First line: ')
while line:
    lines.append(line)
    line = input('Next line: ')
print(lines)

If you get the input from some source all at once, you can use

the_input.split('\n')

To take multiple lines of input and put them in a list of strings, you can use sys.stdin.readlines() which will keep accepting returns until you give it an EOF [ctrl + d in *nix, ctrl + z in Windows].

E.g.:

user_input = sys.stdin.readlines("Favourite foods followed by EOF:") # User gives input... 
    print(user_input)
Output:
    >> ["Spam\n", "Spam\n", "Spam\n"]
Obviously this leaves you with newlines, so you could do something hacky like:
    user_input = [line.rstrip() for line in sys.stdin.readlines()]
Which will give you:
    >> ["Spam", "Spam", "Spam"]

Sounds like an interesting ML problem, though dealing with a list of strings may complicate things significantly. You might want to make them one long string using something like join, e.g.

" ".join(user_input) # Used with a separator of " ", but you could use newlines or something

Which gives one string of:
    >> "Spam Spam Spam"