Multi-dimensional arraylist or list in C#?

You can create a list of lists

   public class MultiDimList: List<List<string>> {  }

or a Dictionary of key-accessible Lists

   public class MultiDimDictList: Dictionary<string, List<int>>  { }
   MultiDimDictList myDicList = new MultiDimDictList ();
   myDicList.Add("ages", new List<int>()); 
   myDicList.Add("Salaries", new List<int>()); 
   myDicList.Add("AccountIds", new List<int>()); 

Generic versions, to implement suggestion in comment from @user420667

  public class MultiDimList<T>: List<List<T>> {  }

and for the dictionary,

   public class MultiDimDictList<K, T>: Dictionary<K, List<T>>  { }

  // to use it, in client code
   var myDicList = new MultiDimDictList<string, int> ();
   myDicList.Add("ages", new List<T>()); 
   myDicList["ages"].Add(23);
   myDicList["ages"].Add(32);
   myDicList["ages"].Add(18);

   myDicList.Add("salaries", new List<T>());
   myDicList["salaries"].Add(80000);
   myDicList["salaries"].Add(100000);

   myDicList.Add("accountIds", new List<T>()); 
   myDicList["accountIds"].Add(321123);
   myDicList["accountIds"].Add(342653);

or, even better, ...

   public class MultiDimDictList<K, T>: Dictionary<K, List<T>>  
   {
       public void Add(K key, T addObject)
       {
           if(!ContainsKey(key)) Add(key, new List<T>());
           if (!base[key].Contains(addObject)) base[key].Add(addObject);
       }           
   }


  // and to use it, in client code
    var myDicList = new MultiDimDictList<string, int> ();
    myDicList.Add("ages", 23);
    myDicList.Add("ages", 32);
    myDicList.Add("ages", 18);
    myDicList.Add("salaries", 80000);
    myDicList.Add("salaries", 110000);
    myDicList.Add("accountIds", 321123);
    myDicList.Add("accountIds", 342653);

EDIT: to include an Add() method for nested instance:

public class NestedMultiDimDictList<K, K2, T>: 
           MultiDimDictList<K, MultiDimDictList<K2, T>>: 
{
       public void Add(K key, K2 key2, T addObject)
       {
           if(!ContainsKey(key)) Add(key, 
                  new MultiDimDictList<K2, T>());
           if (!base[key].Contains(key2)) 
               base[key].Add(key2, addObject);
       }    
}

Not exactly. But you can create a list of lists:

var ll = new List<List<int>>();
for(int i = 0; i < 10; ++i) {
    var l = new List<int>();
    ll.Add(l);
}

you just make a list of lists like so:

List<List<string>> results = new List<List<string>>();

and then it's just a matter of using the functionality you want

results.Add(new List<string>()); //adds a new list to your list of lists
results[0].Add("this is a string"); //adds a string to the first list
results[0][0]; //gets the first string in your first list