How to get all of the supported file formats from Graphics unit?

When any TGraphic descendant registering its own graphic file format with a class procedure TPicture.RegisterFileFormat(), they're all stored in Graphics.FileFormats global variable.

Too bad that FileFormats variable is not in the "interface" section of "Graphics.pas", so I can't access it. I need to read this variable to implement a special filter for my file-list control.

Can I get that list without manual fixing the Graphics.pas's source code?

You are working with a file-list control, and presumably thus a list of filenames. If you don't need to know the actual TGraphic class types that are registered, only whether a given file extension is registered or not (such as to check if a later call to TPicture.LoadFromFile() is likely to succeed), you can use the public GraphicFileMask() function to get a list of registered file extensions and then compare your filenames to that list. For example:

uses
  SysUtils, Classes, Graphics, Masks;

function IsGraphicClassRegistered(const FileName: String): Boolean;
var
  Ext: String;
  List: TStringList;
  I: Integer;
begin
  Result := False;
  Ext := ExtractFileExt(FileName);
  List := TStringList.Create;
  try
    List.Delimiter := ';';
    List.StrictDelimiter := True;
    List.DelimitedText := GraphicFileMask(TGraphic);
    for I := 0 to List.Count-1 do
    begin
      if MatchesMask(FileName, List[I]) then
      begin
        Result := True;
        Exit;
      end;
    end;
  finally
    List.Free;
  end;
end;

Or, you could simply load the file and see what happens:

uses
  Graphics;

function GetRegisteredGraphicClass(const FileName: String): TGraphicClass;
var
  Picture: TPicture;
begin
  Result := nil;
  try
    Picture := TPicture.Create;
    try
      Picture.LoadFromFile(FileName);
      Result := TGraphicClass(Picture.Graphic.ClassType);
    finally
      Picture.Free;
    end;
  except
  end;
end;

Update: if you want to extract the extensions and descriptions, you can use TStringList.DelimitedText to parse the result of the GraphicFilter() function:

uses
  SysUtils, Classes, Graphics;

function RPos(const ASub, AIn: String; AStart: Integer = -1): Integer;
var
  i: Integer;
  LStartPos: Integer;
  LTokenLen: Integer;
begin
  Result := 0;
  LTokenLen := Length(ASub);
  // Get starting position
  if AStart < 0 then begin
    AStart := Length(AIn);
  end;
  if AStart < (Length(AIn) - LTokenLen + 1) then begin
    LStartPos := AStart;
  end else begin
    LStartPos := (Length(AIn) - LTokenLen + 1);
  end;
  // Search for the string
  for i := LStartPos downto 1 do begin
    if Copy(AIn, i, LTokenLen) = ASub then begin
      Result := i;
      Break;
    end;
  end;
end;

procedure GetRegisteredGraphicFormats(AFormats: TStrings);
var
  List: TStringList;
  i, j: Integer;
  desc, ext: string;
begin
  List := TStringList.Create;
  try
    List.Delimiter := '|';
    List.StrictDelimiter := True;
    List.DelimitedText := GraphicFilter(TGraphic);
    i := 0;
    if List.Count > 2 then
      Inc(i, 2); // skip the "All" filter ...
    while i <= List.Count-1 do
    begin
      desc := List[i];
      ext := List[i+1];
      j := RPos('(', desc);
      if j > 0 then
        desc := TrimRight(Copy(desc, 1, j-1)); // remove extension mask from description
      AFormats.Add(ext + '=' + desc);
      Inc(i, 2);
    end;
  finally
    List.Free;
  end;
end;

Update 2: if you are just interested in a list of registered graphic file extensions, then, assuming List is an already created TStrings descendant, use this:

ExtractStrings([';'], ['*', '.'], PChar(GraphicFileMask(TGraphic)), List);