As a follow-up to my post on the LED Christmas tree lights, here's a link to a DIY menorah for all you chosen people. The microchip serves as candle holder, and lights up the LEDs in the right order. [Make]
@Polyphonic: Rabbi Tzvi Pesach Frank forbade the electric Chanukiah on the grounds that the "fuel" (electricity in this case) is not immediately present, but produced at need. Meaning that he would not necessarily have forbidden its use if it was powered by a battery. His other objection was that a light bulb is not fire, but since they *are* considered fire in other contexts, that's always been seen as a relatively weak objection, hence his need for another reason (though admittedly the LEDs used in this case re-raise that question).
Rabbi Ovadia Yosef, in Torat HaMoadim, Siman 5:5, wrote that while you could not make a blessing on an electric Chanukiah, you could use it to fulfill your obligation if no other means was available.
No real Rabbi will tell you it's ideal, but opinions in Judaism are way too varied for an answer on such an esoteric topic to be a straightforward "no" according to *everyone*.