CliWrap. A library to effective launch external processes. This is a great alternative to rolling your own with
Cocona - A superb console application framework.
Dapper - A rational alternative to Entity Framework. Highly recommended. (Dapper powers StackOverflow's file IO for its 6k-per-second requests.)
FluentEmail - A fluent email API with lots of options.
HTMLAgilityPack - Don't use RegEx to parse HTML, use this library.
Humanizer - "Humanize" values in a number of ways (eg, format a date of less than 24 hours ago to "yesterday").
Microsoft.Extensions.Configuration - Very good application configuration with lots of options.
NewtonSoft.Json - A full-featured Json serializer/deserializer. Not needed as much with .NET 5/6 but a life-saver for .NET Framework 4.x.
NodaTime - A better way to work with dates.
Quartz - A job scheduling library.
Serilog - Good logging package.
SharpZipLib - Programatically zip/unzip files.
ShortId - Generate short, unique ids.
xunit A unit testing framework.
YamlDotNet - I don't always parse Yaml, but when I do I use YamlDotNet.