How fast does your internet have to be for you to do your job?

If all you're doing is moving text around then faster internet isn't going to help any. Unless you're streaming video or doing a few other high bandwidth activities then even really shitty broadband is going to service your needs just fine.

Nobody is only moving text around, occasionally (how often depends on the type of work) you need to move a lot of data. In that case a low speed connection stops you in your tracks.

But who just moves text around? Work frequently requires the use of Hangouts, Skype, GoToMeeting, Dropbox, etc. If you have to work through a VPN, the latency added by poor service is a serious drain on productivity.

Total aside: If you experience poor Google Hangouts video quality - use wired connections on both ends of the connection.

So you've not had to do a big code pull from source control or something like Maven or the "Go-lang" builder?

Being done in a few seconds is much more fun (and productive) than being done in a few minutes.