foreach(var item in items)
{
    if (object.ReferenceEquals(item, data))
    {
       // something like this items.Remove(item); should happen here
    }

public IEnumerable<T> Remove<T>(IEnumerable<T> enumeration, T toRemove)
{
    return enumeration.Except(new[] { toRemove });
}

annoyingEnumeration = this.Remove(annoyingEnumeration, annoyingItem);

public IEnumerable Remove(IEnumerable enumeration, object toRemove)
{
    foreach (var e in enumeration)
    {
        if (!object.ReferenceEquals(e, toRemove))
        {
            yield return e;
        }
    }
}

public static class ExtensionMethods
{
    public IEnumerable Without(this IEnumerable enumeration, object toLeaveOut)
    {
        foreach (var e in enumeration)
        {
            if (!object.ReferenceEquals(e, toLeaveOut))
            {
                yield return e;
            }
        }
    }
}

annoyingEnumeration = annyingEnumeration.Without(annoyingItem);

var result = new List<object>();
foreach(var item in items)
{
    if (!object.ReferenceEquals(item, data))
    {
       result.Add(item);
    }
}

var filtered = items.Where(i => !object.ReferenceEquals(i, data));

var custom = new ArrayList();

foreach(var item in items)
{
    // invert the check
    if (!object.ReferenceEquals(item, data))
    {
       // add on the custom result
       custom.Add(item);
    }
}

return custom;

public static System.Collections.IEnumerable Remove<T>(this System.Collections.IEnumerable collection, T data)
{
    foreach (var item in collection)
        if (!object.ReferenceEquals(item, data))
            yield return item;
}

collection = collection.Remove(data);