The boundary for quantum mechanical behavior and classical mechanical behavior To what size and how does "quantum weirdness" such as entanglement and superposition stop applying to larger objects (mere unions of these quantum particles). How do these macro objects that behave as classical mechanics not function like the very particles that they are made of?
 A: The real world is fundamentally quantum mechanical, just like it is fundamentally relativistic, but in certain limits it exhibits a different, simpler behavior.  In the case of relativity there is a natural scale $c$, the speed of light, some constant of the universe.  When we try to consider the physics that happens at speeds much smaller than this scale ($v \ll c$) a simpler sort of theory emerges: newtonian mechanics.
In much the same way, there is another fundamental scale in the universe $\hbar$, a constant that governs how the universe evolves.  But, like in the case of relativity, if we consider phenomenon that happen at a scale very different than $\hbar$ a different sort of theory emerges.  $\hbar$ has the units of action, which are a little harder to conceptualize than velocity, but the idea is the same.  While the universe may be quantum mechanical in nature, in certain limits a different sort of effective theory emerges: classical physics.
In the order of magnitude or dimensional analysis sense, what is important is how $\hbar$, the natural quantum action compares to a typical action for the system of interest.  
A procedure for figuring out whether quantum mechanical effects should be important would be to create a dimensionless ratio involving $\hbar$ and other parameters of your problem and see if that quantity turns out to be very small or very large, at which point quantum effects are unlikely to be important.
Let's try it out with a basketball type object in Earth's gravitational field.  We'll need three dimensionful parameters describing our object, let's take its mass ($m$), earth's gravitational acceleration ($g$) and its size ($R$). With these four parameters we can form a single dimensionless ratio.
$$ \frac{\hbar^2}{m^2 g R^3} \sim 10^{-66} $$   
which for a 1 kg object which is 10 cm across we get for the value of this ratio something like $10^{-66}$, a very very small object.  So we are safe assuming that any physics question we ask about the ball and gravity and any human scale distances doesn't depend on quantum mechanics to get the answer right.
Next let's imagine an electron in an atom, for it we'll take as our dimensionful constants its mass $m_e$, it's charge $e$ the electric constant $k = 1/4\pi\epsilon_0$ and a typical atomic distance $a_0$ the angstrom with these 5 parameters we can form a single dimensionless ratio (we need another one compared to last time since we brought and independent dimension, electrical charge, into the mix): 
$$ \frac{\hbar^2}{ m a_0 k e^2 } \sim 0.5 $$
which comes out close to one, so we would expect quantum mechanical effects to be very important.
Next how about a gas made up of molecules with mass $m$ at temperature $T$, include boltzmann's constant $k_B$, and a pressure $P$.  From these we can form a single dimensionless ratio
$$ \frac{ \hbar^6 P^2}{ m^3 (k_B T)^5 } $$
which for something like nitrogen in a room at room temperature and pressure gives something like $10^{-17}$, again very small, so the air in my room is very classical, but for something like helium, at 1 atm, and at 1 K we get 0.1, so again quantum mechanical effects should be important.
A: Short answer: There is no such boundary.
Longer one:
Quantum Mechanics has been experimentally seen to work even at macroscopic size like neutron stars (whose stability is explained by Pauli's Exclusion Principle). Another example, conduction of macroscopic number of electrons in superconducting Josephson junction (whose BCS theory is purely quantum mechanical) has been experimentally seen.
One more point to note is usually, it is seen that at higher temperature, things become purely classical.
For details, go to 
1.Quantum Classical Transition on Trial
2.Decoherence and the transition from quantum to classical 
A: Quantum weirdness never stops to exist. Some quantum mechanical weirdness in theory could happen but the probability would be ridiculously small. There are just so many wavefunctions interacting with each other and the end result is modelled by Classical Mechanics as its approximation.
When does this start to be apparent? When do you decide if you are going to use QM or CM? The answer is more philosophy than physics. In my opinion there is no real boundary that gives a clear transition. The approximation though really makes sense when you consider a quite large number of particles and at big enough scales, so thats a good indication as if you could use CM in this case. 
So to summarise, there is no real boundary, its just that at some scales the quantum effects are so tiny that are negligible for the accuracy we want to achieve in our everyday lives.
