Print tree level by level including Empty node
A few small changes:
Python has a styleguide, PEP8, which programmers are recommended to follow. One of its recommendations is to use lower_case names for both variables and functions. camelCase is also accepted, if applied consistently (which it is in your code).

Your if conditions in the while loop repeatedly check if node exists. Just put all of them in if node:. Additionally, the checks for node.left and node.right are basically identical, they can be combined by looping over for n in [node.left, node.right]:.

Whenever you do a buffer.pop(0) you probably want a collections.deque. While for lists, popping on the left is O(n) and O(1) on the right, both operations are O(1) for a deque.

Python has the nice feature of multiple assignments, allowing things like:

count, nextCount = nextCount, 0


You are always creating an instance of a node and directly afterwards you assign the value. It is better to add a parameter for the value to the class definition:

class Node:
    def __init__(self, value=0):
        self.value = value
        self.left = None
        self.right = None




With these changes I get this code:

from collections import deque

class Node:
    def __init__(self, value=0):
        self.value = value
        self.left = None
        self.right = None


def printTree(root):
    buf = deque()
    output = []
    if not root:
        print '$'
    else:
        buf.append(root)
        count, nextCount = 1, 0
        while count:
            node = buf.popleft()
            if node:
                output.append(node.value)
                count -= 1
                for n in (node.left, node.right):
                    if n:
                        buf.append(n)
                        nextCount += 1
                    else:
                        buf.append(None)
            else:
                output.append('$')
            if not count:
                print output
                output = []
                count, nextCount = nextCount, 0
        # print the remaining all empty leaf node part
        output.extend(['$']*len(buf))
        print output

if __name__ == "__main__":
    root = Node(1)
    leftNode = Node(2)
    root.left = leftNode
    rightNode = Node(3)
    root.right = rightNode
    leftleftNode = Node(4)
    leftNode.left = leftleftNode
    rightleftNode = Node(5)
    rightNode.left = rightleftNode
    rightrightNode = Node(6)
    rightNode.right = rightrightNode

    printTree(newRoot)




This is still not very efficient code. If you give Node a magic method to decide if it is True or False, your code can be greatly simplified. This method is called __nonzero__ in python 2.x and __bool__ in python3.x.

class Node:
    def __init__(self, value='$', left=None, right=None):
        self.value = value
        self.left = left
        self.right = right

    def __nonzero__(self):
        return self.value != '$'

    def __str__(self):
        buf, out = [self], []
        while buf:
            out.append("{}".format([node.value for node in buf]))
            if any(node for node in buf):
                children = []
                for node in buf:
                    for subnode in (node.left, node.right):
                        children.append(subnode if subnode else Node())
                buf = children
            else:
                break
        return "\n".join(out)

if __name__ == "__main__":
    root = Node(1, Node(2, Node(4)), Node(3, Node(5), Node(6)))
    print root


This gets rid of all the counting and so on. It does, however, not print the last line of all missing nodes (which seemed odd to me anyways). Normally I would use None for an empty Node, not '$', but it also works this way.

I also added left and right, as parameters to the Node, allowing a nested definition, which might be less readable if it becomes too big, but might come handy, when quickly generating a tree like here.

If you also add the magic method __str__ to Node, you can just do print root (or any other node and all its subnodes).

If you insist on having each level printed like a list (to ease copy&amp;pasting it), replace the line 

out.append(" ".join(str(node.value) for node in buf))


with

out.append("{}".format([node.value for node in buf]))


If you want to learn more about magic methods, have a look here.