Q:

What damage does a car suffer if not regularly used?

Sometimes I use the car on daily basis, but there are months when I don't use it at all, and it sits parked outside for 5+ weeks, with the battery disconnected. (Main reasons: working from home that time, excellent coverage of city by public transport.)
But friends say that sitting unused for longer time is not good for the car and it should be used at least once per two weeks. Is it true? What parts/systems can deteriorate in condition if not frequently used?
Some additional information:

Make: Opel Zafira B
Fuel: main: CNG (compressed natural gas), secondary: petrol (seamless switching between the two)1
City climate: mild (winter -5°C (23°F), summer: 29°C (84°F))

          1) note: bi-fuel came from manufacturer (no modifications); CNG fuel is different from LPG

A:

As a general rule of checking, three things; the battery, anything that is rubber (serpentine belt, tyres) and the fluids (oils, coolant).  
Battery: Even if you disconnect the battery, it cannot retain all the juice inside forever and it will drain eventually. This will reduce its life.
Engine: Your various belts and wires can get corroded if not used over a long period; the serpentine belt can get corroded, some animal can chew up the wire or do damage when it's resting.
Your valves and cylinder walls might get corroded due to lack of any oil or movement inside.
Brakes: This happened to me personally where they lose their grip over time.
The above things can go bad, additionally your wheels can get jammed if not used for months, and if you are near a coastal area, your can can be prone to faster corrosion.
Electrical: Sometimes the interior electricals tend to develop a fault such as the power windows get jammed, electric seats. 
AC Gas leak: Cars that are not used over a long time might cause ineffective cooling from the Air Conditioner and will need to be recharged.
Fluids: Most of the fluids, like engine oil/brake fluid, break down, they lose their ability to lubricate eventually though this takes much much longer like half a year or so; but still you will need to replace them.
Since yours is a CNG vehicle, check if the hoses are fine and have not developed a leakage. I would also advise to use petrol if it's going to be intermittent usage since the gas does not lubricate the engine component such as valves as much as petrol; this will not cause any serious harm but it's better to use petrol for a few miles initially and then switch to LPG.
A car is designed to be run like a horse, you cannot get a horse and make it stand all day, you don't buy a horse to pet it, they are meant to be ridden else they will develop problems (or whatever horses become if not ridden).

A:

Friends say that sitting unused for longer time is not good for the car and it should be used at least once per two weeks. Is it true? 

This is absolutely true. The biggest thing to worry about here is dried out seals. When a seal (like an engine rear main seal and differential seals) are left unused for long periods of time, the dry out. When this happens and you use the vehicle, it has a tendency to rip/tear the seals and can cause massive oil leaks. These seals are usually in bad spots where you cannot easily get to them, which means they cost to get replaced.

Condition of what parts/systems can deteriorate if not frequently used?

CNG will not go bad over time, mainly because it's a closed system. The gas (petrol) on the other hand will. Two easy ways to help prevent issues. 1) Top off the fuel tank prior to known periods of the "long sit". This helps prevent the fuel from absorbing water and causing rust issues in the tank. 2) Utilize a fuel stabilizer to keep the fuel fresh. Most of these stabilizers will keep fuel fresh for a year or longer, depending on how it's used.
I already mentioned seals, so won't reiterate here.
When you do use the car, you want to ensure the engine is completely warmed up and used completely warm for several miles (10 or more). When you just run the vehicle for a short period of time, moisture tends to form inside the engine crankcase. This moisture can cause pitting and corrosion on internal engine parts. By running it up to temperature, you are in essence boiling the water away (causing it to evaporate) where it won't cause you any issue.
If you know it it going to be sitting, you need to purchase a battery tender. This is a small battery charger which keeps your battery levels up to where they should be. It also helps with the condition of your battery. By using it, the battery will stay in as good of condition as it can. When you go out to start your vehicle, disconnect (many have quick disconnects which come with them) and your car should start right up.
Brake rotors friction surfaces may become slightly rusted over the long period of time. This should not be anything to worry about. It is basically a surface rust which will be worn off during your first run with the vehicle. You may want to not over tax the brakes (get into a situation where you really need them) until they are cleaned off, but it shouldn't cause any issues. You will not want to use your parking brake, as brakes can become rusted to the disk/drum and won't want to release. Park your car on a flat surface and it shouldn't be an issue.

A:

Any time the car sits idle, the tires develop flat spots. The longer it sits, the worse they get. The vast majority of tires on passenger vehicles are steel-belted radials: while the steel belts offer a high degree of strength, they do bend straight over time.
If you drive every other week the flat spots will round out no problem with enough driving to heat the engine up to normal. If the car sits for too long they can become permanent. While the tire will still work, there will be an annoying sound from them when you drive and they will be out of balance as well.
As another answer said it is important to drive a car 10+ miles every two or three weeks for other maintenance benefits: this is also true of tires.
Cold temperatures exacerbate this issue: if you have cold winters I highly recommend driving the car weekly because it pops out those flat spots, tops off the battery charge, oils up the internal engine seals, and everything else that driving does. This is critical in cold winter months because the low temperatures take whatever problems cars normally have, and makes them worse (battery drains faster, tire flat spots are harder to undo, etc).
I have two vehicles. One is my beater commuter car which I drive several times per week, the other is my nicer car that I drive less. However, I make sure to drive it at least once per week for the reasons outlined in this and other answers and I never have any "sat too long" problems.
Anecdote: the last car I bought had sat on the dealership lot for three months. The tires developed flat spots and had to be replaced (cheap factory tires anyway which had poor traction), and that was during the summer.

