Random Walk simulator seems slow, are there ways to optimize my code?
trials = [0] * 100
for i in range(100):
    trials[i] = randomWalk(200)



You don't need to create a list of zeroes in order to create a list of random walks.  Just use a list comprehension:

trials = [randomWalk(200) for _ in xrange(100)] # In Python3, you should use range().



sum = 0.
for trial in trials:
    sum += trial
avg = 0.
avg = sum / len(trials)



You shouldn't use sum as a variable name because it conflicts with the built-in function.  You know what?  You can use that built-in function:

avg = sum(trials, 0.) / len(trials)



print avg



I'm assuming that you are using Python2 just because of that line (and because of the decimal points in your numbers).  If you put parentheses around avg, your program would run in both versions.  Since I used xrange() above which is not around in Python3, you can't now; but you could also use range() up there to make it bothways-compatible.  range() takes up more memory than xrange(), in Python2, but with only a hundred numbers, it shouldn't really make much difference anyway.