What is the JSON.NET equivalent of XML's XPath, SelectNodes, SelectSingleNode?

Json.NET has SelectToken. It uses a syntax similar to DataBinder.Eval to get JSON via a string expression:

JObject o = JObject.Parse("{'People':[{'Name':'Jeff'},{'Name':'Joe'}]}");

// get name token of first person and convert to a string
string name = (string)o.SelectToken("People[0].Name");

Or if you wanted to select multiple values:

JObject o = JObject.Parse("{'People':[{'Name':'Jeff','Roles':['Manager', 'Admin']}]}");

// get role array token of first person and convert to a list of strings
IList<string> names = (string)o.SelectToken("People[0].Roles").Select(t => (string)t).ToList();

Documentation: Querying JSON with SelectToken

Do you have an object hierarchy that you can map the the JSON? You could create an object tree (i.e. deserialize the JSON), and use LINQ's Where, SelectMany, etc.