An Air conditioner will do the same work for less.
Any of the energy star dehumdifiers will help with energy costs.
My dehumidifier has a humidity sensor on it and goes on and off as it senses the humidity level. It also has a hose on the back and drains directly into the basement sink, no buckets to empty ever.
Cherry

I have a Danby DDR583R (replaced by DDR586R), which is energy star rated.
I used it a couple summers so far and it really does the job. Somewhat quiet too, but you don't want it by the TV set.

I can't comment on how much savings it will be over an older dehumidifier though.

-jasper

Here is a link that might be useful: Basement Dehumidifier

I will check into the Danby. Anyone else care to recommend a dehumidifier?

If you go to the energystar.gov site at the link below and look on the right side of the page at the product list, you'll see how a lot of them stack up in efficiencies. Gives you some idea's anyhow what to look for.

fwiw..;
I have three portable dehumidifiers, Maytag and Fedders, all 3 were made by the exact same china man. 45pt and 65pt units.

They all match that chart at energystar ... i checked each of them for Liters per kWh with the help of a little kill-a-watt meter.
What I discovered is they all greatly lose efficiency below 60%/80F. Even so the larger ones are much more efficient at L/kWh removed than the smaller one at lower RH settings.

I forget exactly but my units are all rated prox 1.7L/Kwh @60%rh/80F .. and thats exactly correct from my tests.
But lower the setting to 50% and the 65pint units were around 1.4L/Kwh and the 45pt unit is 1L/KWh.
Lower the air temp below 80F and they drop in efficiency below that.

Here is a link that might be useful: EnergyStar.gov Dehumidifiers

"I forget exactly but my units are all rated prox 1.7L/Kwh @60%rh/80F .. and thats exactly correct from my tests.
But lower the setting to 50% and the 65pint units were around 1.4L/Kwh and the 45pt unit is 1L/KWh.
Lower the air temp below 80F and they drop in efficiency below that."

So this means exactly what? I have an old 40 pint/24 hours dehumidifer that draws 7.2 amps. Similar amperage ratings are found on the new "Energy Efficient Models" Ahh, to me electric usage is usage in a 24 hour period. Calculating how much moisture the unit removes in comparison to Kw/h is useless and dependent on the % of humidity, and ambient temperature or some other unknown. If your RH is 85% sure it may remove a liter in a Kw/H, but so might a block of ice with a fan blowing over it. However as you have stated as the RH drops so does the efficiency. The truth is you MIGHT save yourself $30 a year on operating costs because of design changes and higher efficiency coils, compressors, and refrigerate. More typically you can expect to add $15 to $20 month in electric operating costs in a typical setting, relative to your location, climate, and local rates. IMHO some of this energy star stuff is nothing more than a marketing gimmick to increase sales. With the shortened longevity of all of these newer products, you never recoup the cost in the form of energy savings over there life. Instead your repurchasing the product sooner and spending more money than you would have otherwise spent in energy usage. It's good for the corporate bottom line and keeps those offshore imports rolling right in.