As of November 2014 all new cars in the EU must have some sort of tyre surveillance system (TPMS). There are basically two different types available and it depends on how they measure tyre pressure, you have indirect and direct TPMS. Both systems are in place to improve our safety on the road, so use TPMS to stay safer.

Direct TPMS
For the direct TPMS, there are sensors that measure the tyre pressure from within the tyre. You can also measure the spare tyre. This then requires that you have sensors mounted in all your wheels. This is a great system, as you can see which tyre is loosing pressure. In some cases even see the actual tyre pressure.
Indirect TPMS
The indirect TPMS measures the difference in wheel rotation through the ABS-system. Early systems could not differentiate between the tyres, but would only indicate that you had an underinflated tyre. New systems can detect which tyre is under-inflated.
Direct vs Indirect
Direct TMPS is a far superior system than indirect MPS, as it is more exact, more details and faster to get a warning signal in case of problems. . The indirect is however a cheaper system, as you don’t need sensors for all you wheels, which in a lot of cases would be 9 sensors. This is to cover a set of summer tyres a set of winter tyres and your spare tyre. You also have problems with the sensors getting damaged, running out of battery or other unexpected problems. The simplicity of the indirect might however make it the dominant system on the market as car manufactures adopt the new technology. If you have a flat tyre and you are using direct TPMS you can not repair the tyre with a instant repair spray can, as this can damage the sensors. This is important to remember.
Run flat technology
It can add a lot of value if your tyres have run flat technology, as you might not otherwise notice that you have a flat, but with TPMS you would get a notice that your tyre has problem.

This is important as you can drive with run-flat tyres, but not more than 70-80 km and not faster than 80km/h. It is more so that you can safely get to a tyre shop to have the tyres repaired and not left stranded on some deserted highway or in a place where it is difficult to change tyres. When you use run flat tyres, it is extremely important that you have a TPMS on your car. With run flat tyres you might not notice that you have a problem and keep driving at your normal speed. This can lead to that the tyre explodes and can easily cause accidents.
TPMS to stay safer
There is still a need to do a visual inspection at least monthly to check that the tyres are free from any visual damages. It is important to check the sidewalls for any bulging or cuts. Check also if the tread pattern looks ok. You can still have uneven wear resulting from that the wheels are not correctly aligned.
The reasoning behind why it is has become mandatory is due to the importance of having correctly inflated tyres. Your driving safety is dependent on having correct tyre pressure, both maneuverability and braking distance is dependent on it. The risk of having your tyres destruct due to excessive hear build up, ply separation and potential explosion is prevented by having proper tyre pressure. Then you have personal benefits in terms of longer tyre life, lower fuel consumption.
So use your TPMS, but also remember that you need to do visual checks to stay safe on the roads.