<p>Is there such a thing? </p>

<p>I'm talking about something like a C++ <code>new</code> command i.e. allocation of memory which necessitates explicit releasing of the memory (or risk memory leaks).</p>

<p>I ask because I remember having to solve some GDI leak problems previously by setting forms/controls/other objects to <code>Nothing</code> but can't remember what or why now...</p>

<p>Do we ever have to worry about memory management when developing in VB6?</p>

I'd like to say you never have to worry about memory management, but it's not quite true.  It depends to some extent on the execution environment that your VB6 code is running in.  I have certainly seen VB6 classes running under COM+ that would leak memory if they didn't explicitly set object references to Nothing when finished with them.
Environmental issues aside, memory that you allocate within the VB6 type system will generally be cleaned up for you.  I'm talking about things you allocate with the New keyword.  But there is a significant exception, pointed out by rpetrich and others: -
Because of the reference-counting mechanism that VB uses to manage the lifetime of allocated objects, it is possible to leak memory if you have any cyclic references.  For example, A->B->C->A.  If you have that kind of scenario you'll probably need to spot it yourself and cure it by explicitly setting references to Nothing.  I am not aware of any tools that help much with identifying this kind of problem.
Further problems come in when you're using libraries written in other languages.  You might New-up a COM object written in C++ that allocates some memory internally, and find that you have to call a particular method (such as Close) to free that memory.  Maybe such a COM object would be badly-written, but plenty of them exist.
So there are no rules to follow, except perhaps: -
Try to know as much as possible about the behaviour of any libraries you use, and
Always run your code while watching a memory trace in Performance Monitor to make sure its memory usage isn't growing in an unbounded fashion.
Try to be aware of cyclic references ;-)