I'm in need of new tires and I saw some fuel efficient/low rolling resistance tires. Is there any disadvantage to this type of tire?
Any tyre design is a balance between cost, grip, longevity, water displacement and rolling resistance. Change one, and chances are you'll adversely affect the others...
Personally, I would always put grip and water displacement (which affects wet grip) above all the others on a priority list. The difference between those "fuel efficient" tyres and normal ones will probably be only a couple more miles per gallon, but if they don't grip as well, don't last as long or cost more to buy, that small saving will quickly vanish...
TRB Special Report 286
2006 report (free PDF) by Transportation Research Board of National Academy of Science in response to request of the U.S. Congress concludes that there is no evidence that any marginal trade off in traction (possibly necessary to achieve lower rolling resistance) would make significant difference in safety, and as long as tyre conforms to UTQG (Uniform Tire Quality Grading) system (grade A wet traction rating for most passenger cars).
Same thing with tread wear. Two tyres of comparable UTQG wear rating, would get comparable mileage within the same operating conditions. As long ratings are similar, and reduced rolling resistance clearly achieved not by reducing initial tread depth.
Given those two being equal in comparing to regular tyre, and average mileage driven, at the low estimate of 1% fuel economy improvement (6 U.S. gallons per year), automobilist should see his extra investment returned within first year.
For the average driver seeking replacement tyres it makes sense to go after LRR ones, provided same UTQG ratings (or similar international standards). A lot of OEMs already use those tyres at the factory (including popular models, e.g. 2010 Ford Fusion), so direct replacements should be fine.
Information on rolling resistance is not (yet) required to be explicitly stated on the tyre or its packaging but should be easily available via spec sheet through the dealer or manufacturer (roughly, 10% improvement in RR translates in 1–2% improvement in fuel-economy).
That said, proper tyre inflation and maintenance are still important as ever both for safety and fuel economy.
Note on RR specification. TireRack.com tech article states:
Tire Rolling Resistance Force is measured in pounds or kilograms of resistance. Comparing Rolling Resistance Force provides a direct way to compare tires of the same size, as well as offers an accurate means of comparing differently sized tires to one another.
Tire Rolling Resistance Coefficient is calculated by dividing the measured rolling resistance force by the tire size’s prescribed load during the test. Comparing Rolling Resistance Coefficients only allows comparing tires within a single size. Tire Rolling Resistance Coefficient does not allow comparing different sized tires.
General tips on tyre maintenance, and how to read sidewall markings (including UTQG ratings) could be found in NHTSA tyre safety brochure. For some general information on recent advances in tyre technology see this article from “The Economist”. See Wikipedia article on LRR tyres for more information and some tyre ratings from Consumer Reports.
It depends a little on your driving style and the typical conditions in your area.
If you get a lot of rain, snow or ice, or you like to drive or corner at speed - don't use them. Go for high grip tyres. You are better off playing it safe than cheap.
If you live somewhere dry, with little traffic, and like to drive slowly - they could be good for you, but won't save you a huge amount. You might be better off just inflating your tyres by a couple of extra psi - this will reduce rolling resistance.