C# – Overriding Equals() but not checking all fields – what will happen

If I override Equals and GetHashCode, how do I decide which fields to compare? And what will happen if I have two objects with two fields each, but Equals only checks one field?

In other words, let's say I have this class:

class EqualsTestClass
{
    public string MyDescription { get; set; }
    public int MyId { get; set; }

    public override bool Equals(object obj)
    {
        EqualsTestClass eq = obj as EqualsTestClass;
        if(eq == null) {
            return false;
        } else {
            return MyId.Equals(eq.MyId);
        }
    }

    public override int GetHashCode()
    {
        int hashcode = 23;
        return (hashcode * 17) + MyId.GetHashCode();
    }
}

I consider two objects Equal if they have the same MyId. So if the Id is equal but the description is different, they are still considered equal.

I just wonder what the pitfalls of this approach are? Of course, a construct like this will behave as expected:

        List<EqualsTestClass> test = new List<EqualsTestClass>();

        EqualsTestClass eq1 = new EqualsTestClass();
        eq1.MyId = 1;
        eq1.MyDescription = "Des1";

        EqualsTestClass eq2 = new EqualsTestClass();
        eq2.MyId = 1;
        eq2.MyDescription = "Des2";

        test.Add(eq1);
        if (!test.Contains(eq2))
        {
            // Will not be executed, as test.Contains is true
            test.Add(eq2);
        }

As eq2 is value-equal to eq1, it will not be added. But that is code that I control, but I wonder if there is code in the framework that could cause unexpected problems?

So, should I always add all public Fields in my Equals() Comparison, or what are the guidelines to avoid a nasty surprise because of some bad Framework-Mojo that was completely unexpected?