AppVeyor is well integrated with Github, free for open-source projects and really easy to set up.
Builds are configured using YAML or UI. Free accounts are limited to one build at a time. Deployment to NuGet is supported, as well as project and account feeds. It is deeply integrated with GitHub, for example allows creating releases. It supports build matrices, AssemblyInfo patching, rolling builds, build prioritization, status badges, build notifications etc.
Travis is well-known CI (and seems to be the most popular hosted CI by far), now it supports building C#, F# and VB projects too. The caveat is that it supports only Linux and Mono and it's in beta ("may be removed or altered at any time").
MyGet is a hosted package server, but now it supports Build Services too (currently preview) and other features. It's free for public feeds (500 MB max) and has slightly better features for approved open-source projects (bigger storage and gallery). Build service is optimized for packages: NuGet feed, MyGet feeds, SymbolSource integration etc.