I have heard from a friend that many people rent a nameserver for their domains. If I understand this well, then it should be a sort of company that has lot of nameservers and lets people hire such a server for their domains.

This interests me a lot, but can someone give me a short explanation of how it works ?
Does anyone know such a company that is reliable ? If possible in Europe (I live in Belgium).

What these DNS must have as features if I'd consider renting it, is that must be able to create subdomains and e-mail forwarding addresses.

PowerDNS with the web interface.

check out http://www.powerdns.net for the "demo".

What these DNS must have as features if I'd consider renting it, is that must be able to create subdomains and e-mail forwarding addresses.

Well there are many companies out there that give you web interfaces to manage DNS and you can even set up a vanity DNS so the nameservers look like your own.
But you mentioned e-mail forwarding.... This is not a feature of DNS. You will need a mailserver for this.
DNS just allows you to setup MX records... that is not forwarding.

Regards,
-Steve

I can host your DNS for you if you want. Just PM me.