Can you transfer music from your iPhone onto iTunes?

I just got a new computer and I want to transfer my music library onto it. None of my songs were bought from iTunes, most of them are via Youtube mp3.Is there any way I can put the music from my phone onto this new computer? I'm afraid to sync it to iTunes because I don't want all of my music to be deleted.

You can try this. It may work. Don't have an iphone, so I'm not sure if it works the same way.
Click the little start/whatever button at the bottom left corner of the screen. Click on Computer.
It should show your iphone as a device or something. Click on it.
Click show files or something like that.
Click on storage. It should show all your music somewhere.
Drag all the music to the music library.
Then you should be able to find an itunes folder and be able to drag all the music from the music library to that folder.
Hope this helped? Sorry if it didn't.

Put the music files on your computer and drag them into itunes, then they should work without deleting everything. If there's no way you can do this, you may need to look into using ssh to get files off your iphone(requires jailbreak)

I'm not 100% sure but I think it will go to your itunes automatically like you mentioned it will sync it will not matter if they are not purchased through itunes. Anything you have on your iphone music wise will be transferred to your itunes once you sink. It will act like an ipod. I have a bunch of music I downloaded elsewhere and on Youtube mp3 and they transfer over fine. They will not be deleted either. It will be on your computer. You may have to try and find the file again to work ( worse case senario but your music is never gone.

Try this http://senuti.org/ This app was designed to move music from an iPod to a computer.

Oh, and consider backing up your itunes library to external storage. And if you paid money for most of the tunes, make a second copy off site. Then if your computer breaks, you can just download the backup to it and you are back in business.