I have just bought my own PS3, after using my brothers for the last few months. I was wondering if I could copy/transfer my profile and saved game data from his PS3 to my new one and if so how to go about doing it. Also, would it have any effect to his PS3 as he has only agreed to let me try it if I know what I'm doing. Can this wipe his PS3? Can I copy my profile and saved data to my PS3? I haven't backed any of it up but both PS3s are fully working.
Copying your profile is simple because profiles are stored on Sony's servers. Just log into your new PS3 with your PSN account and your profile and trophy data should be available. Make sure to sync trophies on your brother's PS3 first.
Saved games are different. As JohnoBoy says, you can use the backup utility and/or a USB drive to copy some save files, but others are copy-protected and cannot be copied this way.
The only way to copy copy-protected save files is to use the cloud service offered by PSN+. Copy-protected saves will be inaccessible for 24 hours after copying them to the cloud, but after this you will be able to download them to your account on your new PS3.
As of right now (November 13th 2012) you can get a 30 day free trial of PSN+ if you "like" them on Facebook. It's only valid for Sony Europe countries (EU/Australia) though. I'm not sure if there is anything similar for the US running at the moment.
You have a couple of options: