Does Python support short-circuiting?

Yep, both and and or operators short-circuit -- see the docs.

Short-circuiting behavior in operator and, or:

Let's first define a useful function to determine if something is executed or not. A simple function that accepts an argument, prints a message and returns the input, unchanged.

>>> def fun(i):
...     print "executed"
...     return i
... 

One can observe the Python's short-circuiting behavior of and, or operators in the following example:

>>> fun(1)
executed
1
>>> 1 or fun(1)    # due to short-circuiting  "executed" not printed
1
>>> 1 and fun(1)   # fun(1) called and "executed" printed 
executed
1
>>> 0 and fun(1)   # due to short-circuiting  "executed" not printed 
0

Note: The following values are considered by the interpreter to mean false:

        False    None    0    ""    ()    []     {}

Short-circuiting behavior in function: any(), all():

Python's any() and all() functions also support short-circuiting. As shown in the docs; they evaluate each element of a sequence in-order, until finding a result that allows an early exit in the evaluation. Consider examples below to understand both.

The function any() checks if any element is True. It stops executing as soon as a True is encountered and returns True.

>>> any(fun(i) for i in [1, 2, 3, 4])   # bool(1) = True
executed
True
>>> any(fun(i) for i in [0, 2, 3, 4])   
executed                               # bool(0) = False
executed                               # bool(2) = True
True
>>> any(fun(i) for i in [0, 0, 3, 4])
executed
executed
executed
True

The function all() checks all elements are True and stops executing as soon as a False is encountered:

>>> all(fun(i) for i in [0, 0, 3, 4])
executed
False
>>> all(fun(i) for i in [1, 0, 3, 4])
executed
executed
False

Short-circuiting behavior in Chained Comparison:

Additionally, in Python

Comparisons can be chained arbitrarily; for example, x < y <= z is equivalent to x < y and y <= z, except that y is evaluated only once (but in both cases z is not evaluated at all when x < y is found to be false).

>>> 5 > 6 > fun(3)    # same as:  5 > 6 and 6 > fun(3)
False                 # 5 > 6 is False so fun() not called and "executed" NOT printed
>>> 5 < 6 > fun(3)    # 5 < 6 is True 
executed              # fun(3) called and "executed" printed
True
>>> 4 <= 6 > fun(7)   # 4 <= 6 is True  
executed              # fun(3) called and "executed" printed
False
>>> 5 < fun(6) < 3    # only prints "executed" once
executed
False
>>> 5 < fun(6) and fun(6) < 3 # prints "executed" twice, because the second part executes it again
executed
executed
False

Edit:
One more interesting point to note :- Logical and, or operators in Python returns an operand's value instead of a Boolean (True or False). For example:

Operation x and y gives the result if x is false, then x, else y

^{Unlike in other languages e.g. &&, || operators in C that return either 0 or 1.}

Examples:

>>> 3 and 5    # Second operand evaluated and returned 
5                   
>>> 3  and ()
()
>>> () and 5   # Second operand NOT evaluated as first operand () is  false
()             # so first operand returned 

Similarly or operator return left most value for which bool(value) == True else right most false value (according to short-circuiting behavior), examples:

>>> 2 or 5    # left most operand bool(2) == True
2    
>>> 0 or 5    # bool(0) == False and bool(5) == True
5
>>> 0 or ()
()

So, how is this useful? One example is given in Practical Python By Magnus Lie Hetland:
Let’s say a user is supposed to enter his or her name, but may opt to enter nothing, in which case you want to use the default value '<Unknown>'. You could use an if statement, but you could also state things very succinctly:

In [171]: name = raw_input('Enter Name: ') or '<Unknown>'
Enter Name: 

In [172]: name
Out[172]: '<Unknown>'

In other words, if the return value from raw_input is true (not an empty string), it is assigned to name (nothing changes); otherwise, the default '<Unknown>' is assigned to name.

Yes. Try the following in your python interpreter:

and

>>>False and 3/0
False
>>>True and 3/0
ZeroDivisionError: integer division or modulo by zero

or

>>>True or 3/0
True
>>>False or 3/0
ZeroDivisionError: integer division or modulo by zero