How to download a Nuget package without nuget.exe or Visual Studio extension?

Either make an account on the Nuget.org website, then log in, browse to the package you want and click on the Download link on the left menu.

Or guess the URL. They have the following format:

https://www.nuget.org/api/v2/package/{packageID}/{packageVersion}

Then simply unzip the .nupkg file and extract the contents you need.

Although building the URL or using tools is still possible, it is not needed anymore.

https://www.nuget.org/ currently has a download link named "Download package", that is available even if you don't have an account on the site.

(at the bottom of the right column).

Example of EntityFramework's detail page: https://www.nuget.org/packages/EntityFramework/: (Updated after comment of kwitee.)

Based on Xavier's answer, I wrote a Google chrome extension NuTake to add links to the Nuget.org package pages.

To obtain the current stable version of the NuGet package use:

https://www.nuget.org/api/v2/package/{packageID}

I haven't tried it yet, but it looks like NuGet Package Explorer should be able to do it:

https://github.com/NuGetPackageExplorer/NuGetPackageExplorer

(or like Colonel Panic says, 7-zip should probably do it)