Include using System.Numerics and add a reference to System.Numerics to the project.

using System;
using System.Numerics;

namespace Euler_25
{
    class Program
    {
        static void Main(string[] args)
        {
            BigInteger l1 = 1;
            BigInteger l2 = 1;
            BigInteger current = l1 + l2;
            while (current.ToString().Length < 1000)
            {
                l2 = l1;
                l1 = current;
                current = l1 + l2;
            }
            Console.WriteLine(current);
        }
    }
}

This simple algorithm iterates through Fibonacci numbers until it reaches one at least 1000 decimal digits in length, then prints it out. This value is significantly larger than even a ulong could hold.

Theoretically, the only limit on the BigInteger class is the amount of RAM your application can consume.

Note: BigInteger is only available in .NET 4.0 and higher.