Are you following godaddy's FTP instructions, and what brand is your router?
Try setting data connection type to PASV (passive mode)
There may be more to it than that:
Modern FTP clients will select passive, or active FTP mode automatically, so this is not usually an issue. However, most FTP servers support active, and passive modes, and give you the choice. GoDaddy has configured ProFTP to only serve in passive mode, and there's a caveat with that:
Some modern routers, and high speed modem/router devices block passive FTP, or one part of it, on their firewalls. The answer is to let that part through your firewall. To test this, turn off all your firewalls, then try to narrow down which one it is. I can tell you that on OS X Yosemite it is not the Mac's firewall.
If it's your own router inside the service provider's device, you need to refer to the manufacturer's support information, or some other online resource.
If it's your ISP's device, you may have limited control over the firewall, and be unable to filter exactly what you want. In other words, you may have to turn the firewall off. Personally I find it unacceptable that GoDaddy is engaging in this silliness, but that's them, and they've always been a pain in the ass for real Webmasters, and Systems Administrators.
As an example: My ISP is Rogers, in the suburbs of Toronto. I have a very fast, and mostly reliable connection. However, I just switched modems to an Hitron CGN3, or CGN3ROG, if you like (note the 'ROG' suffix). I don't have complete control over the firewall, but I have some. If I turn off the blocking of P2P sharing, which I'd rather not, passive FTP works. Obviously this is some odd reasoning at Hitron where they consider passive FTP some kind of P2P sharing. But there you go.
Sussing out this answer required chatting with a very 'trying to be helpful', and patient, support tech at GoDaddy for about three hours, terminating at 2:44am. Eventually he queried a more techy tech, and he determined that one part of the passive FTP protocol was failing. From there I was able to run it into the ground.
You will note, please, that this has nothing to do with the FTP client software (FileZilla, Cyberduck, whatever), and that GoDaddy's FTP server does work as it should. It's just a combination of odd decisions on the parts of GoDaddy, and some device manufacturers.