Back End Developer
ASP.NET MVC
Website: http://www.asp.net/mvc
Source code: http://aspnetwebstack.codeplex.com/
Most of our application runs on top of ASP.NET MVC, so for me it's really important to know it. I think it's a good framework, with a lot of extensibility points, good implementation of the MVC pattern, and we use it in heavy traffic projects without particular problems. Of course there are few things I don't like of it (first of all System.Web), but fortunately the vNext will solve these "problems".
ASP.NET WEBAPI
Website: http://www.asp.net/web-api
Source code: http://aspnetwebstack.codeplex.com/
ASP.NET Web API is probably the best solution if you know ASP.NET MVC and you don't have time to learn something else like NancyFx, NodeJs and so on; The approach is very similar to MVC (Controller + Action). Fortunately it doesn't have the dependency to System.Web but it's a Framework totally separate from MVC and sometime you have to duplicate the same code on MVC and Web API because the same interface/class has a different namespace.
SignalR
Website: http://www.asp.net/signalr
Source code: https://github.com/SignalR/SignalR
I'm not sure if an another Framework for real time applications exists in .NET world, but surely SignalR it is the most famous and used. Build by the same team of ASP.NET MVC / Web API it offers several clients (iOS and Android withXamarin, Windows 8 and Windows Phone) and finally it supports old browsers (with fallback of course forever-frame, polling and son on).
NancyFX
Website: http://nancyfx.org/
Source code: https://github.com/NancyFx/Nancy
Nancy is a lightweight framework for building HTTP based services on .Net and Mono (yes it runs on linux and OSX). The main difference between Nancy and Web API is the routing approach. It uses lambdas to identify relative paths and arguments. Really helpful if you can't deploy on a Windows Server.
Common Logging
Website: http://netcommon.sourceforge.net/
Source code: https://github.com/net-commons/common-logging
I really like this library. When I need to deploy my code side by side with another application or I have to use a specific logging framework, Common Logging is the perfect solution. It is an abstraction of different logging implementations like Log4net, NLog, Enterprise library or whatever you want (you can write your custom bridge). Like many frameworks in the .NET world, this is a porting of a Java Framework (here more info). Really useful!
Windsor Container
Website: http://www.castleproject.org/
Source code: https://github.com/castleproject/Windsor
Probably the first package I add in a new project. I'm really a Dependency Injection addicted and Castle Windsor fits very well with my needs. It's fast, easy to use, all needed lifecycle and offers lot of extension point (Interceptor, custom lifecycle, factories and so on).
Automapper
Website: http://automapper.org/
Source code: https://github.com/AutoMapper/AutoMapper
In my Italian blog I wrote about the importance to use a DTO for the views and the responses instead of the Domain Model. Automapper is absolutely the best framework to "copy" data from an entity to a DTO. Easy to use, fast and extensible it's the second package I install on a new project. A must.
Service Stack
Website: https://servicestack.net/
Source code: https://github.com/ServiceStack
An extremely interesting set of Frameworks. It contains a Json serializer, ORM, Redis client and Service Clients. This set of Frameworks matches perfectly with those who are obsessed with performance. The tagline of the Framework is "Simplicity at Speed". Here a good presentation about ServiceStack and performances in .NET application
Quartz.NET
Website: http://www.quartz-scheduler.net/
Source code: https://github.com/quartznet/quartznet
Quartz.NET is a job scheduling system for small or large applications. Like Common Logging, this is a porting from a Java project (here more info). It offers several ways to run a job, from Cron pattern to special calendar, or whatever you like. The nice thing is you can have a storage for your jobs (configurable SQL, Mongo, MySql .....) very useful for scalable applications.
Cache Cow
Source code: https://github.com/aliostad/CacheCow
Caching is really important, specially if you application must answer to lot of requests. The best way to keep performance acceptable is to reduce the number of operation, specially if request and response are the same for most of the total requests. Cache Cow is a Framework built by my Twitter friend @aliostad and it offers an easy way to cache HTTP requests (both from client and server) using WEB API. With few line of code, you can have a good caching in your favorite storage (Redis, Azure Caching, Sql Server and so on).
Redis
Website: http://redis.io/
Source code: https://github.com/antirez/redis
Redis is an open source caching Framework that offers an advanced Dictionary (key/value) storage. Recently it's available (as preview) also on Windows Azure (here a good article explains how to use redis with MVC and Azure). The Performance of this Framework are great: it is very fast, and it also available on distributed infrastructures. If you go in a multi-server application, probably it is the best solution.
XUnit
Source code: https://github.com/xunit/xunit
This is the most active testing framework for .NET applications. It's used on lot of the Frameworks mentioned in this post (MS Stack included). It has support for Resharper, CodeRush Test Runner and Xamarin Test Runner.
Autofixture
Source code: https://github.com/AutoFixture/AutoFixture
It's a framework that helps developers to do Test-Driven Development by automating non-relevant Test Fixture Setup. Really I'm not a fan of TDD but Autofixture contains several features like Automock (helpful if you change frequently the constructor dependencies) and AutoMoqData that can help all developers.
Sharp Tests Ex
Source code: http://sharptestex.codeplex.com/
It's a library born to wrap all testing framework using a fluent syntax. Usually I don't change often the testing framework but sometime I need to copy part or my code to an existing application that uses NUnit or MS-Test. In this case the only thing to do is change the Testing attribute in the test class.
Front End Developer
Sass
Website: http://sass-lang.com/
Source code: https://github.com/sass/sass
Sass (Syntactically Awesome Style Sheets) is an extension to CSS. It is CSS as it should have been. Its key features are the ability to use variables, nesting, mixins and loops within your code. This means you can code more quickly and keep your code neat, tidy and easy to maintain. The Sass or SCSS code you write is then compiled in to standard CSS as browsers can't (yet) understand Sass / SCSS.
Also take a look at Compass, it is a great framework for Sass that contains loads of reusable mixins... no more memorising vendor prefixes and obscure pre-spec CSS3 styles!
Bootstrap
Website: http://getbootstrap.com/
Source code: https://github.com/twbs/bootstrap
Created by the guys at Twitter, Bootstrap gives you a massive selection of reusable, robust and attractive styles for your everyday styling needs. It includes a responsive, mobile-first grid system, basic typography styles, styles for common elements such as buttons and form inputs and lots more. Bootstrap is perfect for rapid prototyping but don't use it for everything otherwise we'll end up with all sites looking the same!
Bower
Website: http://bower.io/
Bower is a front-end package management tool, you use it to speed up your dev workflow. It allows you to simply install packages and their dependencies in your project using the command-line. No more Googling for the latest version of jQuery, downloading it, unzipping it, copying it into your project etc... just:
$ bower install jqueryGrunt
Website: http://gruntjs.com/
Source code: https://github.com/gruntjs/
Like Bower, Grunt is another dev tool that can be run from the command-line. It is a JavaScript task runner which allows you to automate pretty much anything... minification, unit testing, compiling of Sass, code linting, image compression, launching a node server, creation of documentation, whatever you like. There are many, many Grunt Plugins available which do the most common tasks so it is easy to get started.
Yeoman
Website: http://yeoman.io/
Source code: https://github.com/yeoman/yeoman
Yeoman makes using Grunt and Bower even easier. It allows you to scaffold out a project very quickly using a "Generator". The Generator will create a bare-bones (boilerplate) project architecture, with certain libraries, frameworks, Grunt tasks and Bower dependencies pre-installed. Different Generators are available for different projects. For example if you are starting a new AngularJS app, you would use the Angular Generator and run
$ yo angular and it will set up the architecture, along with basic units tests, install AngularJS and Bootstrap (if you want it).AngularJS
Website: https://angularjs.org/
Source code: https://github.com/angular/angular.js
AngularJS is an open-source MVC JavaScript framework created by Google - it allows you to very quickly extend HTML's capabilities and create powerful, highly testable web applications. Angular includes two-way declarative data-binding which greatly simplifies complex application development as much of the DOM manipulation is handled automatically by the framework. It is (fairly) well documented and there is an active support community on Stack Overflow.
Karma
Website: http://karma-runner.github.io/
Source code: https://github.com/karma-runner/karma/
Karma (formerly Testacular) is a framework agnostic test runner. You write your unit tests alongside your application code and you can automatically test your code as you develop. Karma allows you to test your code in real browsers on real devices or in PhantomJS. It is definitely worth watching the introduction video from creator Vojta Jína.
Jasmine
Website: http://jasmine.github.io/
Source code: https://github.com/pivotal/jasmine
Jasmine is a framework for testing JavaScript code. You can use Jasmine to write your unit tests and then run them using Karma. The syntax of Jasmine is very clear and easy to understand, yet powerful.
If you want to take things further take a look at Jest (by Facebook), it is built on top of Jasmine, and adds some additional levels to Jasmine's feature-set.