Element-wise addition of 2 lists?

Use map with operator.add:

>>> from operator import add
>>> list( map(add, list1, list2) )
[5, 7, 9]

or zip with a list comprehension:

>>> [sum(x) for x in zip(list1, list2)]
[5, 7, 9]

Timing comparisons:

>>> list2 = [4, 5, 6]*10**5
>>> list1 = [1, 2, 3]*10**5
>>> %timeit from operator import add;map(add, list1, list2)
10 loops, best of 3: 44.6 ms per loop
>>> %timeit from itertools import izip; [a + b for a, b in izip(list1, list2)]
10 loops, best of 3: 71 ms per loop
>>> %timeit [a + b for a, b in zip(list1, list2)]
10 loops, best of 3: 112 ms per loop
>>> %timeit from itertools import izip;[sum(x) for x in izip(list1, list2)]
1 loops, best of 3: 139 ms per loop
>>> %timeit [sum(x) for x in zip(list1, list2)]
1 loops, best of 3: 177 ms per loop

The others gave examples how to do this in pure python. If you want to do this with arrays with 100.000 elements, you should use numpy:

In [1]: import numpy as np
In [2]: vector1 = np.array([1, 2, 3])
In [3]: vector2 = np.array([4, 5, 6])

Doing the element-wise addition is now as trivial as

In [4]: sum_vector = vector1 + vector2
In [5]: print sum_vector
[5 7 9]

just like in Matlab.

Timing to compare with Ashwini's fastest version:

In [16]: from operator import add
In [17]: n = 10**5
In [18]: vector2 = np.tile([4,5,6], n)
In [19]: vector1 = np.tile([1,2,3], n)
In [20]: list1 = [1,2,3]*n
In [21]: list2 = [4,5,6]*n
In [22]: timeit map(add, list1, list2)
10 loops, best of 3: 26.9 ms per loop

In [23]: timeit vector1 + vector2
1000 loops, best of 3: 1.06 ms per loop

So this is a factor 25 faster! But use what suits your situation. For a simple program, you probably don't want to install numpy, so use standard python (and I find Henry's version the most Pythonic one). If you are into serious number crunching, let numpy do the heavy lifting. For the speed freaks: it seems that the numpy solution is faster starting around n = 8.