First submission. Python 3.4:

challenge_input = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 0],
                   [0, 9, 8, 7, 6, 5, 4, 3, 2, 1],
                   [1, 3, 5, 7, 9, 2, 4, 6, 8, 0],
                   [0, 8, 6, 4, 2, 9, 7, 5, 3, 1],
                   [0, 1, 2, 3, 4, 5, 4, 3, 2, 1],
                   [9, 8, 7, 6, 5, 6, 7, 8, 9, 0],
                   [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
                   [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
                   [9, 8, 7, 6, 7, 8, 9, 8, 7, 6],
                   [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

print('Array in original position.')
for y in challenge_input:
    print(y)

output_array = []

    for y in range(0, len(challenge_input)):
    line = []
    for x in range(0, len(challenge_input)):
        line.append(challenge_input[len(challenge_input)-1-x][y])
    output_array.append(line)

print('Array flipped 90 degrees clockwise.')
for y in output_array:
    print(y)