Is there any way of transferring Minecraft worlds onto another computer?

Yes there's get a usb and put it in the port of the computer with the world on it and go to the search bar thing when you click the windows key then type in %appdata% and search it then go to minecraft and i forget the rest just look for worlds in the minecraft folder and move it to the usb and just put the usb in the other computer and do the %appdata% thing again and go to worlds and open up a world you don't care about and replace all the files inside it with the ones inside the world you want to put on the other computer

Indeed there's. Your local worlds (single player) are saved in your minecraft folders. To get to it the full shortcut (For windows) is; Computer/Harddisk(generally C. /Users/(Username)/Appdata/Roaming/.mi…
For win7 you can go to the bottom of the start menu and type in %appdata%, then hit enter, it will take you right to the Roaming folder.

The folder you then want is called saves, copy and paste that using a USB stick, an external harddrive, burn to optical media, use a cloud storage site, whatever strikes your fancy.

If you ever run your own server you can then paste worlds from the server into that folder to access them in single player, or download world files that have been posted online showcasing impressive builds.

Yeah all you need to do is to close your eyes. Take a mouse and slap it against your balls