Hi,

I would like to make my personal web site with asp.net with any databases

Is it possible to register my domain and host in free of cost?

You might look into Microsoft office live. The basic service is free. I'm not sure what database capabilities are included for free.

Check it out at http://office.microsoft.com/en-us/office...

Unfortunately no, but with http://www.4clickdesigns.com you get a free domain name with you hosting, it was a cheaper option for me.