I've used a PICAXE powered via serial; diode mix RTS with DTR, and run through a low-dropout 78L05(100mA) to power the PICAXE.
For laptop use, the diode drop and regulator overhead may be a problem, but if RTS and DTR never exceed 6V then the PICAXE can be powered without the regulator - but take care never to plug it into any +12V/-12V serial port ! [ Maybe a 5.V zener across the supply would help ? ]
The big question is, how much current can be drawn from RTS or DTR, and there's no easy answer to that, but it's probably reasonable to say about 10mA per line, 20mA when diode mixed. That's enough to run a PICAXE and even some LED's when 1K8 or 2K2 LED limiting resistors are used ( they are usually still bright enough ).