Código Delphi [-]
...
implementation 

uses Unit2;

procedure TForm1.Button1Click(Sender: TObject);
begin
  Form2:= TForm2.Create(Self);
  Form2.UrlToImage(Edit1.Text, Form2.Image1);
  Form2.Label1.Caption:= Edit2.Text;
  Form2.ShowModal;
end;
end.

Código Delphi [-]
...
type
  TForm2 = class(TForm)
  ...
  public
    procedure UrlToImage(const URL:string; aImage:TImage);
  end;
...

implementation 

uses jpeg;

procedure TForm2.UrlToImage(const URL:string; aImage:TImage);
var
  s: string;
  MStream: TMemoryStream;
  JPGImg: TJPEGImage;
begin
  try
    s:= idHTTP1.Get(URL);
  except
    raise Exception.Create('Error: No se encontró la imágen');
  end;
  MStream:= TMemoryStream.Create;
  JPGImg:= TJPEGImage.Create;
  try
    MStream.Write(s[1], Length(s));
    MStream.Position:= 0;
    JPGImg.LoadFromStream(MStream);
    aImage.Picture.Assign(JPGImg);
  finally
    MStream.Free;
    JPGImg.Free;
  end;
end;
end.

Código Delphi [-]
uses Urlmon;
//...........................................................................
procedure LoadURLImage(Image: TImage; URL: String);
var
  TempName: String;
begin
  TempName:= 'temp' + ExtractFileExt(URL);
  URLDownloadToFile(nil, PCHAR(URL), PCHAR(TempName), 0, nil);
  Image.Picture.LoadFromFile(TempName);
  DeleteFile(TempName);
end;

Código Delphi [-]
LoadURLImage(Image1, 'http://telmosilva.files.wordpress.com/2010/03/informatica_12.jpg');