It surprises me that this hasn't been mentioned yet, so for the sake of completeness...
You can perform list unpacking with the "splat operator": *, which will also copy elements of your list.
old_list = [1, 2, 3]
new_list = [*old_list]
new_list.append(4)
old_list == [1, 2, 3]
new_list == [1, 2, 3, 4]
The obvious downside to this method is that it is only available in Python 3.5+.
Timing wise though, this appears to perform better than other common methods.
x = [random.random() for _ in range(1000)]
%timeit a = list(x)
%timeit a = x.copy()
%timeit a = x[:]
%timeit a = [*x]
#: 2.47 µs ± 38.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
#: 2.47 µs ± 54.6 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
#: 2.39 µs ± 58.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
#: 2.22 µs ± 43.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)