Follow the below Steps, to connect CRM Online or On-Premise using C#,

Step 1: Include the below References in your project, you can get the same from Latest SDK. Open SDK and goto the path, SDK –> Bin for the dlls

Microsoft.Crm.Sdk.Proxy
Microsoft.Xrm.Sdk

Step 2: Include the below Framework Assemblies in your project,

System.Runtime.Serialization
System.ServiceModel

Step 3: Finally add the below namespaces in your class file,

using Microsoft.Crm.Sdk.Messages;
using Microsoft.Xrm.Sdk;
using Microsoft.Xrm.Sdk.Client;
using System.ServiceModel.Description;

Your References will be looking like this in Solution Explorer,

Step 4: Use the Below Method to your code for establishing CRM Connection, which consists of 3 parameters

static IOrganizationService _service;

public static void ConnectToMSCRM(string UserName,string Password,string SoapOrgServiceUri)
{
    try
    {
        ClientCredentials credentials = new ClientCredentials();
        credentials.UserName.UserName = UserName;
        credentials.UserName.Password = Password;
        Uri serviceUri = new Uri(SoapOrgServiceUri);
        OrganizationServiceProxy proxy = new OrganizationServiceProxy(serviceUri, null, credentials, null);
        proxy.EnableProxyTypes();
        _service = (IOrganizationService)proxy;
    }
    catch (Exception ex)
    {
        Console.WriteLine("Error while connecting to CRM " + ex.Message);
        Console.ReadKey();
    }
}

Step 5: For this example, I am using Console application. Finally the code looks like this,

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using Microsoft.Crm.Sdk.Messages;
using Microsoft.Xrm.Sdk;
using Microsoft.Xrm.Sdk.Client;
using System.ServiceModel.Description;
namespace ConnectToCRM
{
   class Program
   {
       static IOrganizationService _service;
        static void Main(string[] args)
       {
           ConnectToMSCRM("arunpotti@XYZORG.onmicrosoft.com", "XYZORGPassword", "https://XYZORG.api.crm5.dynamics.com/XRMServices/2011/Organization.svc");
           Guid userid = ((WhoAmIResponse)_service.Execute(new WhoAmIRequest())).UserId;
           if (userid != Guid.Empty)
           {
               Console.WriteLine("Connection Established Successfully");
               Console.ReadKey();
           }
       }
       public static void ConnectToMSCRM(string UserName,string Password,string SoapOrgServiceUri)
       {
           try
           {
               ClientCredentials credentials = new ClientCredentials();
               credentials.UserName.UserName = UserName;
                credentials.UserName.Password = Password;
               Uri serviceUri = new Uri(SoapOrgServiceUri);
               OrganizationServiceProxy proxy = new OrganizationServiceProxy(serviceUri, null, credentials, null);
               proxy.EnableProxyTypes();
               _service = (IOrganizationService)proxy;
           }
           catch (Exception ex)
           {
               Console.WriteLine("Error while connecting to CRM " + ex.Message);
               Console.ReadKey();
           }
       }
   }
}

Step 6: Build the project and Click on Start, you can see the below output