can you download free full ps3 games without registration?

There's a few you can download on the Playstation Network, but they're poorly made and short. Other ways of getting games are illegal, and besides, the PS3 copyprotection hasn't been broken yet.

There are alternate ways of getting them, and other items if you can't afford the price however. There are several sites that will give you free items, like a PS3 or games, for signing up and completing trial product offers (Some of the offers may cost a few dollars to sign up for, but most are free as long as you cancel them in time).

Just be careful with the sites, as some of them are just out to scam you. Below is the site I used to get my 250Gb PS3 Slim absolutely free. (Also, if you already have a PS3, they have an option to just send the cash cost to you instead.)