The main discussion among contemporary rabbis on the issue of electricity on shabbat is not if using electricity is permitted or forbidden: every Orthodox Rabbi accepts that we are not allowed to directly activate electricity on Shabbat. The debate revolves around the nature of the prohibition: if turning on electricity on Shabbat is a Biblical or a rabbinical prohibition.
"Rabbi David Tzvi Hoffman states what has emerged as the consensus opinion: the verse (Exodus 35:3) "One may not create a fire on Shabbat in all your dwellings" describes the prohibition against creating fire of any sort. Current flowing through a filament and causing it to glow creates fire despite the absence of a "flame" and regardless of whether that which is on fire is consumed... Based on the position of Rambam, which most commentaries accept, the overwhelming majority conclude that turning on an electric light on Shabbat violates the biblical prohibition of lighting a flame." (Rabbi Michael Broyde, see below)
Most modern rabbinic authorities consider that turning on an incandescent light, --an action which heats a metal filament until it glows--violates a Biblical prohibition because it is considered a Toleda (extension) of lighting a fire.
It is important to clarify for the advanced students that unlike other areas of Jewish Law where post Talmudic Rabbis cannot extend the Rabbinical Talmudic prohibitions to other cases (mar-it 'ayin, for example), the extension of a melakha of Shabbat, does not require the particular sanctioning of a Talmudic Bet Din. It is similar to the application of the Toledot of neziqin(torts, damages,etc), where post Talmudic Rabbinical decisors might apply the Talmudic principles learned from ancient cases, extending them to contemporary circumstances.
Shabbat Shalom!
Candle Lighting in NYC: 8:13 PM
Shabbat ends in NYC: 9:20 PM
For a comprehensive analysis and discussion of this matter I recommend the following article The Use of Electricity on Shabbat and Yom Tov by Rabbi Michael Broyde & Rabbi Howard Jachter which appeared in the Journal of Halacha & Contemporary Society, No. XXI - Spring 91 - Pesach 5751