I have here at home a router, like many people out there.
The router is connected with an Ethernet cable that comes from the modem.

But, to prevent hackers or anything else to try bothering me, if I'm not using the router, is removing the Ethernet cable a good security measure? Or it doesn't do that much in security, so I should leave it always connected?

If there is not an internet connection to your device then a hacker is not going to be able to communicate with that device. (Edit: As some have pointed out...this is assuming an attacker is attempting over the internet from a remote location)

With that said, eventually you will have to connect to the internet again if you want to use the internet and if you were to eventually obtain malware on your computer such as a keylogger. That keylogger is going to rely on the internet to send its data back to the hacker. If the keylogger is written properly, when you disconnect, it will just wait for you to connect to the internet again to send its data back to the attacker.

In my opinion, I think disconnecting from your internet will prove to be more of a hassle than a protection. Instead, focus on the security of your device and your actions on the internet. Being a smart internet user can provide a great deal of security to your device.

Elaboration (EDIT):

I do agree that this method with decrease the time of opportunity for an attacker but the reason I chose to put emphasis on endpoint security and user education is because if you imagine an enterprise environment, they have devices and services that rely on an internet connection 24/7. So an enterprise can't rely on disconnecting from the internet as a viable security measure. Instead they focus on securing the devices on the network and the network itself. So I believe this will achieve 2 things: 1) greater security. 2) better user experience(always have internet access on demand) and I believe you can apply these strategies to your personal network as well.
