So, I wanne have a domain pointing to my Raspberry Pi, but as it is at home it has a dynamic IP address.
So, my question is, does somebody know a good&free service to convert from dynamic to static IP? I recall seing something like that but I don't remember where

Your Pi most likely have a 192.168 IP, so you'll have to configure your router to give it a static IP (in the 192.168 range), then do some port forwarding, or even set your Pi as DMZ, then it could use your public IP. Then you can easily give it a domain name, depends if your IP changes once in a while, if so go with no-ip as AssemblyBandit said.

Then you'll want to get no-ip or something, the DNS will change when your IP change. Or if you want a real static IP, you'll have to call your ISP and they'll probably charge extra fees.

You'll have to install a daemon on one of your computers which notices IP changes and changes the DNS accordingly.

Back in the days, I used DynDNS.org for anything like that (as well as for Omni URL, which was omnimaga.dyndns.org until October 2006 then became an alternate URL until Nikky hacked it in Jan 2008), but sadly they shut down their free service in 2011, so yeah I would go with no-ip, although unless it changed from 2004-05, it was incredibly slow and had pop up ads like on Dot.tk.

Does http://freedns.afraid.org/ offer such service too?

on freedns.afaid.org i just read the router could be the update client too
yay, that means i don't have to have so much crap running on my pi