It really depends on what you do and what SSD you get.
Laptop HDDs will typically use 1 Watt while idle (spinning but no read/write activity), 0.005 Watts while asleep (spun down), and 5 Watts when spinning up.
SSDs use varies, with the better drives using about 0.02 Watts idle, 1-2 Watts while reading and writing. Some SSDs use up to 1 Watt idle though.
So if your current laptop usage makes your laptop spin down its HDD a lot, and you get a SSD which consumes a fair amount of power, your power use will likely go up.
But if your current laptop usage leaves the HDD spinning most of the time and/or you get a SSD which consumes little power, your power usage could go down. (The formerly active HDD is now spun down, with its activity replaced by the SSD which has lower idle power consumption.)
The Samsung 850 EVO and Pro and Crucial BX100 are the SSDs currently with the lowest idle power. If you're interested in maximizing your laptop's battery life, those are the drives to get. The Samsungs are around 20-50 mW, the BX100 around 30-80 mW. (This BTW is why I've passed on the many deals on the Crucial M500 SSD for like $180 for a 1 TB drive. The M500 is a decent desktop drive, but its idle power draw is over 1 Watt. A really bad choice for a laptop SSD.)
NerdyComputerGuy :
Ehhh, you've have maybe a little more wattage but considering you are using a laptop all this means is that you battery life will run out faster by not by like 5 minutes or something.
The difference can be substantially bigger. Most laptops are sporting about 40 Watt-hour batteries. If you figure they typically last 5 hours on battery, then you're talking about an average power draw of 8 Watts.
If you're able to reduce the HDD's spinning power draw by putting it to sleep (save 0.995 Watts) and replace it with a SSD with low wattage (0.02 Watts), that's a net reduction of 0.975 Watts. Your laptop which used consume 8 Watts now consumes 7.025 Watts, and your battery life will increase from 5 hours to 5h 41m.
OTOH if you replaced it with a M500 and your power consumption is now 9 Watts, your battery life would decrease from 5 hours to 4h 27m.