Epydoc allows for docstrings on variables:

While the language doesn't directly provides for them, Epydoc supports variable docstrings: if a variable assignment statement is immediately followed by a bare string literal, then that assignment is treated as a docstring for that variable.

Example:

class A:
    x = 22
    """Docstring for class variable A.x"""

    def __init__(self, a):
        self.y = a
        """Docstring for instance variable A.y"""

Well, even though Python does not treat strings defined immediately after a global definition as a docstring for the variable, sphinx does and it is certainly not a bad practice to include them.

debug = False
'''Set to True to turn on debugging mode. This enables opening IPython on 
exceptions.
'''

Here is some code that will scan a module and pull out names of global variable definitions, the value and a docstring that follows.

def GetVarDocs(fname):
    '''Read the module referenced in fname (often <module>.__file__) and return a
    dict with global variables, their value and the "docstring" that follows
    the definition of the variable
    '''
    import ast,os
    fname = os.path.splitext(fname)[0]+'.py' # convert .pyc to .py
    with open(fname, 'r') as f:
        fstr = f.read()
    d = {}
    key = None
    for node in ast.walk(ast.parse(fstr)):
        if isinstance(node,ast.Assign):
            key = node.targets[0].id
            d[key] = [node.value.id,'']
            continue
        elif isinstance(node,ast.Expr) and key:
            d[key][1] = node.value.s.strip()
        key = None
    return d

Sphinx has a built-in syntax for documenting attributes (i.e. NOT the values as @duncan describes). Examples:

#: This is module attribute
x = 42

class MyClass:

    #: This is a class attribute
    y = 43

You can read more in the Sphinx docs: https://www.sphinx-doc.org/en/master/usage/extensions/autodoc.html#directive-autoattribute

...or in this other question: How to document a module constant in Python?

Some python documentation scripts have notation that can be use in the module/classes docstring to document a var.

E.g. for spinx, you can use :var and :ivar. See this document (about half-way down).

No, you can only do this for modules, (lambda and "normal") functions and classes, as far as I know. Other objects, even mutable ones inherit the docstrings of their class and raise AttributeError if you try to change that:

>>> a = {}
>>> a.__doc__ = "hello"
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: 'dict' object attribute '__doc__' is read-only

(Your second example is valid Python, but the string """l""" doesn't do anything. It is generated, evaluated and discarded.)

To add to to ford's answer about Epydoc, note that PyCharm will also use a string literal as the documentation for a variable in a class:

class Fields_Obj:
    DefaultValue=None
    """Get/set the default value of the data field"""

Properties can have docstrings! This covers the most common use case of documenting instance variables.

class A:
    def __init__(self):
        self._x = 22

    @property
    def x(self):
        "document x"
        return self._x

    @x.setter
    def x(self, value):
        self._x = value

A.x.__doc__

A lot of answers assume you want it for offline use and points to sphinx or Epydoc.

But if you want it for runtime use the answer is that is impossible to add an attribute to another attribute. So you can't attach a doctring to variable.

When you do:

a = True
print(a.__doc__)

You'll be getting the docstring for the bool class. In my application I need it for plug-ins. What I do is to use an associated variable/attribute.

Something like this:

a = True
_help_a = "help for a variable"

As this looks ugly what I'm actually using are syntactic macros (take a look a macropy module). The code looks like this:

with document:
    a = True
    """ help for a variable """

I explain the whole idea here

Yes, you can do that!

You can actually 'document' lambdas and variables in a module by attaching docstrings to them.

Not properties. Not class attributes. Variables, constants and lambdas. No Sphinx, no Epydoc. No typing.annotations. Plain old help(). Real docstrings. In the line of

VAR = value # (apply magicka to add docstring 'This is a variable')
help(VAR)   # shows 'This is a variable'

Well, sort of ...

The trick is to use decorators.

You take anything that can hold a docstring (class or function), apply decorator to it, but instead of returning modified class or wrapper class as you usually do with decorators, you can just return an object of completely different class generated on the fly with a docstring attached to it.

Something like this:

# This is ugly, yes, but it's gonna be even uglier, strap in.
@decorator_generator(lambda x: x+1)
class foo: """ docstrings """
# The decorator generator returns a decorator, which, in turn, can return
# ANYTHING AT ALL, which will be assigned to `foo`. We can use that.

The types will be very messy, but, hey, who needs them anyways.

We can also do some module class magic to reattach the docs every time a new value is assigned to module attributes, thus preserving the docs on assignment.

Consider this:

# one.py

# We import sys to use the module magicka later
import sys

def documented_named(baseclass, *init_args, **init_kwargs):
    def _decorator(decorated):
        class _documented_class(baseclass):
            def __str__(self):
                return decorated.__name__
            __doc__ = decorated.__doc__
            def __documented__(self):
                return (documented_named, baseclass, decorated)
        return _documented_class(*init_args, **init_kwargs)
    return _decorator

def documented(baseclass, *init_args, **init_kwargs):
    def _decorator(decorated):
        class _documented_class(baseclass):
            __doc__ = decorated.__doc__
            def __documented__(self):
                return (documented, baseclass, decorated)
        return _documented_class(*init_args, **init_kwargs)
    return _decorator

def documented_lambda(__lambda):
    def _decorator(decorated):
        def _lambda(*args):
            return __lambda(*args)
        _lambda.__doc__ = decorated.__doc__
        return _lambda
    return _decorator


class nopreserve: pass

def documented_ducktype(baseclass, *init_args, **init_kwargs):
    def _decorator(decorated):
        class _documented_class(baseclass):
            __doc__ = decorated.__doc__
            def __documented__(self):
                return (documented, nopreserve, decorated)
        return _documented_class(*init_args, **init_kwargs)
    return _decorator

# Module magix
_thismodule = sys.modules[__name__]
class _preserve_documented(_thismodule.__class__):
    def __setattr__(self, attr, value):
        ex = getattr(self, attr, None)
        if ex is not None and hasattr(ex, '__documented__'):
            decorator, baseclass, decorated = ex.__documented__()
            if baseclass is nopreserve:
                baseclass = value.__class__
            super().__setattr__(attr, decorator(baseclass, value)(decorated))
        else:
            super().__setattr__(attr,value)
_thismodule.__class__ = _preserve_documented

@documented(int, 100)
class VAR1: """ DOCUMENTATION FOR VAR1 """

@documented_named(float, 7.891011)
class VAR2: """ DOCUMENTATION FOR VAR2 """

@documented_lambda(lambda x: x+1)
class LAMBDA: """ LAMBDA DOCUMENTATION PROVIDED HERE """

@documented_ducktype(int, 100)
class VAR3:
    """ DOCUMENTATION FOR VAR3 
    Multiline, eh?
    """

Let's test it like this:

# two.py
import one
from one import VAR2

# inspect is here for convenience only, not needed for docs to work
import inspect

def printvar(v):
    print('str:  ', v)
    print('repr: ', repr(v))
    print('docs: ', inspect.getdoc(v))
    print('')

print('Here you go, documented variables and lambda:')
for v in [one.VAR1, one.VAR2, one.LAMBDA]:
    printvar(v)

# And then we set vars and check again
one.VAR1 = 12345
one.VAR2 = 789

print('\n\nAfter setting VAR1 and VAR2 with <module>.<varname> = foo to new values:')
for v in [one.VAR1, one.VAR2]:
    printvar(v)
print('Cool, the docs are preserved.\n\n')
print('Note that we have also preserved the types, though this is not really necessary:')
print('VAR3:')
printvar(one.VAR3)
one.VAR3 = 'VAR3 is a string now'
print('And after assignment:')
printvar(one.VAR3)

print('VAR2 imported with "from <module> import VAR2":')
printvar(VAR2)

print('However, if we set it here we will obviously loose the doc:')
VAR2 = 999
printvar(VAR2)

print('And the types are terrible:')
print('one.VAR1:  ', type(one.VAR1))
print('one.VAR2:  ', type(one.VAR2))
print('one.LAMBDA:', type(one.LAMBDA))

The output:

$ python two.py
Here you go, documented variables and lambda:
str:   100
repr:  100
docs:  DOCUMENTATION FOR VAR1 

str:   VAR2
repr:  7.891011
docs:  DOCUMENTATION FOR VAR2 

str:   <function documented_lambda.<locals>._decorator.<locals>._lambda at 0x7fa582443790>
repr:  <function documented_lambda.<locals>._decorator.<locals>._lambda at 0x7fa582443790>
docs:  LAMBDA DOCUMENTATION PROVIDED HERE 



After setting VAR1 and VAR2 with <module>.<varname> = foo to new values:
str:   12345
repr:  12345
docs:  DOCUMENTATION FOR VAR1 

str:   VAR2
repr:  789.0
docs:  DOCUMENTATION FOR VAR2 

Cool, the docs are preserved.


Note that we have also preserved the types, though this is not really necessary:
VAR3:
str:   100
repr:  100
docs:  DOCUMENTATION FOR VAR3 
Multiline, eh?

And after assignment:
str:   VAR3 is a string now
repr:  'VAR3 is a string now'
docs:  DOCUMENTATION FOR VAR3 
Multiline, eh?

VAR2 imported with "from <module> import VAR2":
str:   VAR2
repr:  7.891011
docs:  DOCUMENTATION FOR VAR2 

However, if we set it here we will obviously loose the doc:
str:   999
repr:  999
docs:  int([x]) -> integer
int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments
are given.  If x is a number, return x.__int__().  For floating point
numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string,
bytes, or bytearray instance representing an integer literal in the
given base.  The literal can be preceded by '+' or '-' and be surrounded
by whitespace.  The base defaults to 10.  Valid bases are 0 and 2-36.
Base 0 means to interpret the base from the string as an integer literal.
>>> int('0b100', base=0)
4

And the types are terrible:
one.VAR1:   <class 'one.documented.<locals>._decorator.<locals>._documented_class'>
one.VAR2:   <class 'one.documented_named.<locals>._decorator.<locals>._documented_class'>
one.LAMBDA: <class 'function'>

And yes, you can actually import one and get the docs with help(one.VAR1) this way. And I suppose Sphinx and Epydoc can handle that pretty well if they can be forced to ignore the decorator (I did NOT test that).

Note that you can also do something similar with __metaclass__, which should look better syntax-wise, but you'll need Python 3.9 for that.

And I should get a time machine, this WAS totally possible since the decorators were introduced.