How can I install an older version of a package via NuGet?

As of NuGet 2.8, there is a feature to downgrade a package.

NuGet 2.8 Release Notes

Example:

The following command entered into the Package Manager Console will downgrade the Couchbase client to version 1.3.1.0.

Update-Package CouchbaseNetClient -Version 1.3.1.0

Result:

Updating 'CouchbaseNetClient' from version '1.3.3' to '1.3.1.0' in project [project name].
Removing 'CouchbaseNetClient 1.3.3' from [project name].
Successfully removed 'CouchbaseNetClient 1.3.3' from [project name].

Something to note as per crimbo below:

This approach doesn't work for downgrading from one prerelease version to other prerelease version - it only works for downgrading to a release version

Try the following:

Uninstall-Package Newtonsoft.Json -Force

Followed by:

Install-Package Newtonsoft.Json -Version <press tab key for autocomplete>

I've used Xavier's answer quite a bit. I want to add that restricting the package version to a specified range is easy and useful in the latest versions of NuGet.

For example, if you never want Newtonsoft.Json to be updated past version 3.x.x in your project, change the corresponding package element in your packages.config file to look like this:

<package id="Newtonsoft.Json" version="3.5.8" allowedVersions="[3.0, 4.0)" targetFramework="net40" />

Notice the allowedVersions attribute. This will limit the version of that package to versions between 3.0 (inclusive) and 4.0 (exclusive). Then, when you do an Update-Package on the whole solution, you don't need to worry about that particular package being updated past version 3.x.x.

The documentation for this functionality is here.