If your result is going to be a new list, then you can use a list comprehension:
new_list = [ some_function(i, j) for i, j in zip(list1, list2) ]
Here's a real example of the above code:
>>> list1 = [1, 2, 3, 4]
>>> list2 = [1, 3, 4, 4]
>>> like_nums = [ i == j for i, j in zip(list1, list2) ]
>>> print like_nums
[True, False, False, True]
This will make a list of bools that show whether items of the same index in two lists are equal to each other.
Furthermore, if you use the zip function, there is a way to unzip the result when you are done operating on it. Here's how:
>>> list1 = [1, 2, 3, 4]
>>> list2 = [1, 3, 4, 4]
>>> new_list = zip(list1, list2) # zip
>>> print new_list
[(1, 1), (2, 3), (3, 4), (4, 4)]
>>> newlist1, newlist2 = zip(*new_list) # unzip
>>> print list(newlist1)
[1, 2, 3, 4]
>>> print list(newlist2)
[1, 3, 4, 5]
This could be useful if you need to modify the original lists, while also comparing the elements of the same index in some way.