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No-one has given the code I would write, which doesn't create a list but instead tracks the answer in a loop. The logic is a little more complex, but it avoids storing values (here it doesn't really matter, since it's only 10 values, but a similar problem with input from another program, might have more data than fits in memory).

maxOdd = None
for _ in range(10):
    value = int(input('Enter a value: '))
    if (value % 2 and (maxOdd is None or value > maxOdd)):
        maxOdd = value
if maxOdd:
    print('The largest odd value entered was', maxOdd)
else:
    print('No odd values were entered.')

Note that I am treating non-zero values as True, so value % 2 is a test for true (because it gives a non-zero remainder, and Python treats non-zero values as true). Similarly, if maxOdd tests that maxOdd is not None (nor zero, but it cannot be zero, because that is even).

Another way, closer to the other answers, in that it treats the numbers as a sequence, but still avoiding storing everything in memory, is to use a generator:

from itertools import islice

def numbers():
    while True:
        yield input('Enter a value: ')

def odd(n):
    return n % 2

try:
    print('The largest odd value entered was',
          max(filter(odd, map(int, islice(numbers(), 10)))))
except ValueError:
    print('No odd values were entered.')

This is more "advanced", but numbers() creates a generator, and the chain of functions max, filter, map, islice effectively call that for each value (simplifying slightly). So the end result is a kind of pipeline that, again, avoids keeping everything in memory.