Using Stack is the obvious way to traverse tree without recursion. Below is an algorithm for traversing binary tree using stack. See this for step wise step execution of the algorithm.

1) Create an empty stack S.
2) Initialize current node as root
3) Push the current node to S and set current = current->left until current is NULL
4) If current is NULL and stack is not empty then 
     a) Pop the top item from stack.
     b) Print the popped item, set current = popped_item->right 
     c) Go to step 3.
5) If current is NULL and stack is empty then we are done.

Let us consider the below tree for example

            1
          /   \
        2      3
      /  \
    4     5

Step 1 Creates an empty stack: S = NULL

Step 2 sets current as address of root: current -> 1

Step 3 Pushes the current node and set current = current->left until current is NULL
     current -> 1
     push 1: Stack S -> 1
     current -> 2
     push 2: Stack S -> 2, 1
     current -> 4
     push 4: Stack S -> 4, 2, 1
     current = NULL

Step 4 pops from S
     a) Pop 4: Stack S -> 2, 1
     b) print "4"
     c) current = NULL /*right of 4 */ and go to step 3
Since current is NULL step 3 doesn't do anything. 

Step 4 pops again.
     a) Pop 2: Stack S -> 1
     b) print "2"
     c) current -> 5/*right of 2 */ and go to step 3

Step 3 pushes 5 to stack and makes current NULL
     Stack S -> 5, 1
     current = NULL

Step 4 pops from S
     a) Pop 5: Stack S -> 1
     b) print "5"
     c) current = NULL /*right of 5 */ and go to step 3
Since current is NULL step 3 doesn't do anything

Step 4 pops again.
     a) Pop 1: Stack S -> NULL
     b) print "1"
     c) current -> 3 /*right of 5 */  

Step 3 pushes 3 to stack and makes current NULL
     Stack S -> 3
     current = NULL

Step 4 pops from S
     a) Pop 3: Stack S -> NULL
     b) print "3"
     c) current = NULL /*right of 3 */

# Python program to do inorder traversal without recursion
 
# A binary tree node
class Node:
     
    # Constructor to create a new node
    def __init__(self, data):
        self.data = data 
        self.left = None
        self.right = None
 
# Iterative function for inorder tree traversal
def inOrder(root):
     
    # Set current to root of binary tree
    current = root 
    s = [] # initialze stack
    done = 0
     
    while(not done):
         
        # Reach the left most Node of the current Node
        if current is not None:
             
            # Place pointer to a tree node on the stack 
            # before traversing the node's left subtree
            s.append(current)
         
            current = current.left 
 
         
        # BackTrack from the empty subtree and visit the Node
        # at the top of the stack; however, if the stack is 
        # empty you are done
        else:
            if(len(s) >0 ):
                current = s.pop()
                print current.data,
         
                # We have visited the node and its left 
                # subtree. Now, it's right subtree's turn
                current = current.right 
 
            else:
                done = 1
 
# Driver program to test above function
 
""" Constructed binary tree is
            1
          /   \
         2     3
       /  \
      4    5   """
 
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
 
inOrder(root)
 
# This code is contributed by Nikhil Kumar Singh(nickzuck_007)