I'd like install a new Wi-Fi thermostat. The old one didn't have a C-wire but luckily there is an unused wire on both sides (one coming out of the wall and one at the furnace not connected yet), so I am going to use this unused wire as the C-wire. My only concern is that the C terminal at the furnace is already occupied with other two wires (that have nothing to do with the thermostat, but are connected one to the humidifier and the other one not sure to what, probably the air purifier). The question is: can I add a third wire to the C board of the furnace and use it as C-wire for the wi-fi thermostat? See picture: yellow is the unused wire. 
How many wires can be connected to the C terminal at the furnace
furnacethermostat-c-wire
Related Solutions
Yes you can terminate any number of connections on the C terminal. All of the connections will be in parallel. This is very common.
Unfortunately, the Aquastat you're using does not expose a C terminal. The transformer is likely soldered directly to the board; so unless you're good with a solder gun, you're going to have to buy a different thermostat.
The red wire attached to the T terminal, should be connected to the R terminal of the thermostat. The white wire attached to the T terminal, should be connected to the W terminal of the thermostat. When the thermostat calls for heat, it will connect the R terminal to the W terminal. This will cause the coil to pull a switch closed (relay), which tells the boiler that the thermostat is cold.
If you're not afraid to potentially break things, and you really want to try to get the new thermostat working. You could try to add your own C wire. You'll simply have to connect the new C wire, to the other lead of the secondary coil of the transformer.
Left image shows original wiring. Right image shows where the C terminal should be added.
WARNING:
Modifying the wiring of the Aquastat will likely void the warranty, and could potentially damage the equipment. Proceed at your own risk.
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Best Answer
Technically, there should only be one wire connected to the screw terminal. However, it's common practice in the HVAC industry to connect more.
If you want to do it the proper way, you should use a twist-on wire connector (or other connector), and a length of scrap wire to make a pigtail.
You may also want to consider why there are already two wires. It's common in a furnace to have the A/C contactor coil terminated there, but you'll want to figure out where the other wire goes. The concern here, is that you could overload the transformer. If the transformer is operating at or near maximum capacity, the additional load of the thermostat could push it beyond the limit. Best case here would be a blown fuse, worst case being a blown transformer.
If the transformer is powering a humidifier or air cleaner, you'll want to make sure it can handle the additional load of the thermostat (though thermostats are typically a small load).