Although I usually don't like the idea of adding exe's to source control, I would suggest that source control should contain anything that is required in order to open, build and execute the project.
In this case it sounds like the .nuget folder is a required dependency. Therefore it ought to be under source control.
The only question left, that you need to research, is how NuGet is going to react if that folder is marked read-only, which TFS will do once it has been checked in.
I would suggest that probably what you want to do is make NuGet a requirement that has to be installed on every developers workstation.
Further, you should place in source control the batch file required to get a workstation ready to start editing the project. The batch file is going to run the commands necessary to get and install the dependency packages.
Beyond that I'd say you might want to contact NuGet directly to ask them how, exactly, this is supposed to work.
Now that nuget supports package restoration we're looking at it more closely.
We use Subversion for source control, and my initial thoughts are that .nuget should be added to our repository, but added using svn:externals so that it points to a single location.
That way we can automatically push out new versions to all developers and projects. For projects on release branches, rather than HEAD, we can specify the revision of svn:externals reference if we want to leave nuget alone.
We have a lot of projects, so it also means not duplicating nuget.exe multiple times in the repo.
You need to commit .nuget\nuget.targets, but not nuget.exe. The targets will download the exe if it doesn't exist, as long as you change DownloadNuGetExe to true in nuget.targets
@Richard Szalay's answer is right - you don't need to commit nuget.exe. If for some reasons Visual Studio does not automatically download the nuget.exe, make sure you have the following set to true in the nuget.targets file:
<!-- Download NuGet.exe if it does not already exist -->
<DownloadNuGetExe Condition=" '$(DownloadNuGetExe)' == '' ">true</DownloadNuGetExe>
Close the VS solution, reopen it and build it. Visual Studio should download nuget.exe automatically now.
This post is old, you should not be using solution level NuGet package restore anymore. As of version 2.7+ there is an option in the NuGet setup to automatically restore packages on build.
So the .nuget folder can be deleted and the option removed from your projects.
UPDATE: With the release of NuGet 4.x and .NET Standard 2.0, when you use the new csproj format you can now use package references, ironically reintroducing the dependency on msbuild to restore packages, but now packages are a first class citizen of msbuild. The link above also makes mention of the PackageReference, but the following announcement details it better:
UPDATE 2: Apparently with VS2017 you can even use package references with classic csproj projects, but they aren't backwards compatible anymore, and there have been some problems with restoring package sub-dependencies. I'm sure that will all be resolved.