Personally, I would prefer to have them on all the time in my car. But the NHTSA (National Highway Transportation Administration) has done extensive statistical analysis in the USA, and found there is no statistically significant difference (within the margin of error for the statistical sample) in the rate of accidents when DRL's are on or off. Statistical analysis done in some other countries, especially those in more northern latitudes, have shown that DRL's do reduce accidents. As mentioned previously, this probably has something to do with the duration of twilight conditions (longer in northern latitudes).
Regarding energy usage, when the vehicle electrical system is drawing more current, there is more drag on the engine (and causes more fuel to be used) due to the alternator having to generate more amps. The amount of extra drag is slight, but when multiplied by the number of cars on the road, it does add up to more global energy use and more greenhouse gases. I am not endorsing the conclusion that for that reason that DRL's should not be used (I agree the difference is very small), but there is "some" rationale for that position, especially "if" it can be statically determined that DRL's do not decrease accidents.
But aside from extra energy usage, there are others who don't like DRL's for reasons that probably are stronger cases against them:
http://www.motorists.org/drl/reasons-to-oppose
Looks like motorcycle riders are probably behind this group, since it makes them less noticeable if they are no longer the only ones with DRL's. If I ever rode a motorcycle, I would definitely want to be the only ones with DRL's on the road.