There is not too much out there that will generate the type of lighting provided by a halogen lamp. Your best bet is to go with a fluorescent torchiere, or if you can find one, go with LED.

Here is a link that might be useful: BrandNameLighting

Here is a no frills CFL torchiere that we use. It emits plenty of light and the price was right.

Here is a link that might be useful: Torchiere CFL 3 Way

Thanks. I've read about CFL torchieres but been unable to find any. For that price I can try one out without feeling bad if I don't like it!

I have the same question the OP did. I want to get rid of some 300-watt halogen torchieres. But what else like it is that bright? Those with a single Edison socket limit you to a 42w CFL - but that's still nowhere near as bright (or as high quality light) as a halogen bulb. Plus there's that annoying slow CFL ramp-up. Is there anything that has, say, 3 or 4 Edison sockets spaced 5" apart in a triangle or square respectively, so you could put 23w CFLs or cheap sno-cone LEDs in that together would be as bright as an old halogen torch lamp, but use 20% of the power? I don't want anything that requires funky hard-to-get light bulbs or GU24s.