Open multiple Projects/Folders in Visual Studio Code
Update
As mentioned in several other answers here, this 'accepted' answer is outdated and is no longer correct. VS Code now has the concept of a 'workspace' which lets you add several 'root' folders to VS Code in the same window.
For instance, when working on a project in one folder that utilizes shared code held in a different folder, you can now open both the project folder and the shared folder in the same window.
To do this you use the Add folder to Workspace... command. VS Code then saves this configuration in a new file with a .code-workspace extension. If you double-click that file, VS Code will re-open with both folders present.
Original Accepted Answer (Outdated)
As described in The Basics of Visual Studio Code article:
"VSCode is file and folder based - you can get started immediately by opening a file or folder in VSCode."
This means the concept of solution and project files, like the .sln and .csproj, have no real function in VSCode other than that it uses these only to target and identify which language to support for Intellisense and such.
Simply put, the folder you open is the root you work with. But of course there is nothing from stopping you to open multiple windows.
As for the request features options, navigate to Help > Request Features which will redirect you to the UserVoice page of VSCode.
Support for multi-root workspaces is now enabled by default in the latest stable release [November 2017 release].
The File > Add Folder to Workspace command brings up an Open Folder dialog to select the new folder.
Not sure why the simplest solution is not mentioned. You can simply do File>New Window and open the other project in the new window.
Update
This is now available out of the box as of October 2017. From the blog post:
This was our #1 feature request - it's been a while coming but it's here now.
The complete documentation is here.
You can work with multiple project folders in Visual Studio Code with multi-root workspaces. This can be very helpful when you are working on several related projects at one time. For example, you might have a repository with a product's documentation which you like to keep current when you update the product source code.
Original answer
Currently the Insider channel of VSCode gives us this out of the box.
Read more from the blog post.