how can i see how much of the stack space is currently used in my delphi app?

This should give you your current stack usage:

function CurrentStackUsage: DWord;
asm
  mov eax, fs:[4]
  sub eax, esp
end;

I don't remember off the top of my head a simple way to get the max stack size at run-time, but you have the default value in your linker options.

VMmap from SysInternals can give you a graphical view of each type of memory used by your application, including stack. It does not give you the exact usage like the function in Per Larsen's answer, but may help you to visualize memory usage at different stages of your application.

{$IFDEF MSWINDOWS}
function currentStackUsage: NativeUInt;
//NB: Win32 uses FS, Win64 uses GS as base for Thread Information Block.
asm
  {$IFDEF WIN32}
  mov eax, fs:[4]  // TIB: base of the stack
  sub eax, esp     // compute difference in EAX (=Result)
  {$ENDIF}
  {$IFDEF WIN64}
  mov rax, gs:[8]  // TIB: base of the stack
  sub rax, rsp     // compute difference in RAX (=Result)
  {$ENDIF}
{$ENDIF}
end;