We currently don't use nuget for our dependencies, preferring to go old-skool way and stick them all in a libs folder and reference from there. I know. So 1990's.
Anyway, nuget has always made me feel a bit queasy... you know, reliance on the cloud and all that. As such, I'm find myself in the main agreeing with Mark Seeman (see here: http://blog.ploeh.dk/2014/01/29/nuget-package-restore-considered-harmful/) who says:
Personally, I always disable the feature and instead check in all packages in my repositories. This never gives me any problems.
Trouble is, this has changed in version 3, you can't store packages alongside the solution, as outlined here: https://oren.codes/2016/02/08/project-json-all-the-things/. Which sorta screws up checking them into source code.
So, am I worrying about nothing here? Should I drink from the nuget well, or side with Mr Seeman and er on the side of caution?
Storing NuGet packages in source control is a really, really bad idea. I accidentally did it once and I ended up bloating my source code considerably, and that was before .NET Core...
Drink deep from the NuGet well. Most software components are packaged in a similar way these days (NPM, Bower etc). The referenced blog post is two years old and package management is changing rapidly in the .NET world, so here's some of my experience lately.