Here's a rough equivalence:
Dictionary<K,V> <=> hash_map<K,V>
HashSet<T> <=> hash_set<T>
List<T> <=> vector<T>
LinkedList<T> <=> list<T>
The .NET BCL (base class library) does not have red-black trees (stl map) or priority queues (make_heap(), push_heap(), pop_heap()).
.NET collections don't use "iterators" the way C++ does. They all implement IEnumerable<T>, and can be iterated over using the "foreach statement". If you want to manually control iteration you can call "GetEnumerator()" on the collection which will return an IEnumerator<T> objet. IEnumerator<T>.MoveNext() is roughly equivalent to "++" on a C++ iterator, and "Current" is roughly equivalent to the pointer-deference operator ("*").
C# does have a language feature called "iterators". They are not the same as "iterator objects" in the STL, however. Instead, they are a language feature that allows for automatic implementation of IEnumerable<T>. See documentation for the yield return and yield break statements for more information.