Last year, I spent about six months without regular Internet access. It was fascinating watching my muscle memory adjust, and it got me thinking about how I worked in the past. Not just StackOverflow (which I don't find very useful for what I do), but the tendency to immediately google for a library, or current papers on a class of algorithms, or a piece of code I can study to see the preferred idiom for something.
In some ways I was more productive than before, but I tended to reuse less code, and use less sophisticated algorithms and data structures to solve problems. Having good code around to read became a lot more important, as did having access to good books, and good man pages. (It reminded me why I loved OpenBSD so much in the 90s)
The most positive thing that came out of it was reading a lot more code; I realized one of the habits that had diminished most since sometime in the last decade was the habit of reading the source code for something when I had a problem with it, instead of immediately googling it.
It made me think that maybe younger programmers should try working without a connection now and then (say, for a week at a time). Also that open source has really changed things; there's so much stuff that I don't even think about writing myself now, because I know someone out there has already written and open sourced.