Finding the largest product of four consecutive numbers in a grid
It's OK to use max(), reimplementing it yourself won't save time, especially since the Python version is possibly faster if it's written in C. It's possible to be more concise and clearer though: max(hori + verti + dia + diarev).
You should use a list of list to represent a matrix, not a list of dictionaries. As cat_baxter points out, d = [map(int, row.split()) for row in open('20x20.txt').read().splitlines()] is enough to populate d. However if you're not familiar with list comprehensions and map, it's OK to use normal loops.
Python doesn't really have constants, but a convention is to do VERTI = "verti" and then use VERTI everywher, denoting that it is a constant ("verti" is not a good name, by the way, "vertical" is better. Use code completion.)
try: ... except: ... is bad practice, you need to catch specific exceptions (KeyError in this case). And you need to understand why those errors are thrown! This could be a bug in your code.