I live in a hostel where there is no grounded/earthed connection. Will it harm my laptop or charger?
Your laptop is almost certainly of a "class 2" design. Meaning it is electrically double insulated. You can Identify this by checking for a symbol which looks like a square, within a slightly bigger square.
Alternatively, a European GS or VDE standard may have been attached, covering class 2 implicitly.
This covers all Class 2 appliances in europe, and means that the appliance does not need a circuit protective conductor (Green/Yellow earth wire) in order to be used safely.
You will find this on your transformer block between the mains plug and the laptop DC jack. Meaning that both parts are protected from "Direct contact" fault conditions. Now known in Britain as "Basic Protection", as of IET Wiring Regulations 17th edition (2008).
You may find that the earth pin in your plug is there only to facilitate the interface with the socket, and is not actually wired to anything. The cable running from it may also be of a 2-core double insulated design (Phase and Neutral only).
Your laptop is safe. But the building itself is another story entirely. I suggest you avoid having a shower.
I would like to add a comment to Daniel Beck's conversation in the question comments, but do not have sufficient privillages.
The voltage you have measured is the result of a reference point differential, and is unlikely to be capable of carrying a current. This is why the apparent voltage would disappear if you connected the extraneous conductive part of your mac book to the local earth (A grounded reference point).
The metal case of your mac book is separated by two layers of insulating material from any electrical parts by design.
You will also find the Class 2 logo somewhere on your macbook's transformer block.
The ground or earth is there primarily to protect you from electrocution.
So long as your laptop and charger are in good condition, are of double-insulated design, and are used safely (not in the bathtub or shower) you and they will come to no harm.
If the equipment is designed with the expectation that it be earthed, by connecting it to a non-earthed supply you are running a small additional risk that a fault or damage in the equipment may lead, in the worst case, to something exploding in your face or catching fire while you are asleep. These are the sort of risks of death and injury we take every day when crossing the road.
If your laptop charger/adapter says "connect only to grounded outlet", you'd better not do otherwise, because its safety depends on this connection. Example HP PA-1650-02H says that on its label (click to enlarge).
Contrary to what some claim here there are plenty of laptop adapters/chargers that are only class I according to IEC60950-1, meaning they need an earth connection to ensure safety. The aforementioned HP adapter is one such example.
If you have a multimeter/ohm-meter you can easily determine if an adapter/charger is class I by measuring the resistance between its output negative pin and its input earth prong. If that resistance is close to 0 ohms, then it's a class I device. The aforementioned HP adapter, of which I have one sample, indeed measures close to 0 ohms that way.
Note that a class I device can carry nearly all the same certification marks that a class II device, as you can see in the image. The important one that's missing is the square-in-square. That's only present on class II devices.
As an electronics designer I'm confident in saying that very many well known makes of laptop supply (dell, lenovo among others) are certainly NOT double insulated. The VDE mark CERTAINLY DOES NOT mean double insulated, class 1 kit can be VDE approved too. The negative side of the output jack is grounded to mains earth- hence they use a 3 pin cloverleaf mains input. In turn this appears on exposed metal connector shells like USB and VGA. Yes the voltages between the parts within the laptop are low, but fed from an unearthed socket the whole assembly has no direct connection through the power supply to either pole of the mains. Now, if the stray capacitances plus any filter capacitors between the two poles of the mains and the secondary side are roughly equal, then to AC the output will 'float' to about half mains voltage, but this voltage will fall away as soon as much current is drawn (e.g. by a meter). 80VAC from 220V 50Hz is very believable. This 'earth leakage' is certainly enough to damage some powered CMOS USB hubs for example, and you may just about feel it. Please take care when connecting together devices and peripherals fed from a mixture of earthed and un-earthed supplies, if possible its much better to be either all one or all the other.
I remember in the past I was using may laptop which is connected to the internet by Ethernet and the charging cable disconnected.
Once I was walking back to my laptop as soon my hand touched the laptop it discharged electrostatic charge.
After that, the LAN connection was damaged. I think that would have never happened if I had connected the power cable which was earthed.