Lists are a mutable type – in order to create a copy (rather than just passing the same list around), you need to do so explicitly:
listoflists.append((list[:], list[0]))
However, list is already the name of a Python built-in – it’d be better not to use that name for your variable. Here’s a version that doesn’t use list as a variable name, and makes a copy:
listoflists = []
a_list = []
for i in range(0,10):
a_list.append(i)
if len(a_list)>3:
a_list.remove(a_list[0])
listoflists.append((list(a_list), a_list[0]))
print listoflists
Note that I demonstrated two different ways to make a copy of a list above: [:] and list().
The first, [:], is creating a slice (normally often used for getting just part of a list), which happens to contain the entire list, and thus is effectively a copy of the list.
The second, list(), is using the actual list type constructor to create a new list which has contents equal to the first list. (I didn’t use it in the first example because you were overwriting that name in your code – which is a good example of why you don’t want to do that!)