• The dotnet sdk commandline tools support package inspecttion. As of the end of 2018, you can run dotnet list package --outdated.
• Greenkeeper is well-known for NPM package management in the node ecosystem. npm-outdated is also used.
• Dependabot is a commercial service that supports many platforms, including .NET Core.
• Renovate is another commercial multiplatform update automation tool that supports .NET Core.
• dotnet-outdated is a global tool to find outdated packages in .NET Core code. It can also perform updates.

Using Azure DevOps Pipelines and NuKeeper to Automate NuGet Package updates

Scott Hanselman has written on NuKeeper, DotNet Outdated and Dependabot.

Nate McMaster keeps a big list of .NET Core global tools and maintains the CommandLineUtils library that we use to parse the commandline in a manner similar to dotnet and other utilities.