Do orbitals overlap? Yes, as the title states: Do orbitals overlap ?
I mean, if I take a look at this figure...

I see the distribution in different orbitals. So if for example I take the S orbitals, they are all just a sphere. So wont the 2S orbital overlap with the 1S overlap, making the electrons in each orbital "meet" at some point?
Or have I misunderstood something? 
 A: An orbital is essentially a wave function from which a probability distribution of the location of an electron upon measurement can be inferred. What is depicted will be something like the region within which the probability is 50% (shaped in a way that depends on a decomposition of the state function in a radial part and an angular part). 
If you mean to ask if these regions overlap, yes, they certainly do. If you mean to ask if the regions of space where the probabilities are non-zero overlap, they even more certainly do, as the probability is non-zero almost everywhere (i.e. zero on set of volume 0). 
If you mean to ask if they (or rather the spaces they span) in the state space overlap, then no: see Programming Enthusiast's answer.
A: If you mean to ask "do the orbital radial probability distributions overlap?", the answer is yes:

Image Credit

making the electrons in each orbital "meet" at some point

As you can see from the image, the electron orbitals are not position eigentstates.  If you're imagining two point-like electrons in different orbitals colliding, you're not thinking "quantum mechanically".
A: The orbitals shown in the figure are the different eigenstates of the electronic wave functions derived from the solution of Schrodinger equation. One of the postulates of QM states that these eigenstates are independent in a free atom.
Orbitals do overlap when two atoms are close together, e.g. in a molcule and the degree of overlap corresponds to the type of bonding (ionic, covalent etc.). 
A: Yes, orbitals do overlap. However, these orbitals do not necessarily mean that is where the electron is. The orbitals are only the probable locations that an electron would be. In fact, electrons are not even necessarily in those orbitals; they could be anywhere. This is able to be shown mathematically, but it is relatively dense stuff. If you are curious and want a detailed explanation, I would be happy to edit the answer to show all of that.
A: There has been a lot of emphasis on QM when detailing events here. Firstly, it would be beneficial to examine the foundations to modern physics, which are solidly hinged on mathematical pretexts that show significance when relating to various physical phenomenon. Quantum mechanics dwells on mathematical significance as perspectives. But that is not to say, that physical aspects to such measurements can be discounted, or misrepresented in a qualitative analysis.
The waves representative to particles mentioned herein represent radial probabilities, that are cumulative in a sense; rather than measuring electron densities at various points, the objective is to analyse the radial probability which takes into account the cumulative probability of an infinitesimally small volume at a distance r from the center of the nucleus, extended 3 dimensionally over a region encapsulating the nucleus at that distance. This eliminates the need to define the precise location of the electron, and thus, extends the uncertainty to a larger region by focusing on the probability distribution in the region. Hence the observation of the uncertainty principle.
All of the above remains valid so far as measurements and analyses are concerned. Ultimately, there is that certain electron in n=1 and n=2 and so on, and based on the probability distributions, these particles can exist at the same place, but probably at different times, if one is to observe other principles associated to the state of the electron.
Thats right; electrons do have definitive positions at a given time. The uncertainty principle governs measurements only, and is a correct one; we cant measure the position and momentum of an electron precisely, all at once.
