Perhaps not regularly, but certainly whenever the heap begins to look a little dry - successful composting depends on moisture.
There is a very good article on composting and moisture level , together with a host of useful links, here , and an excellent one on home composting, by the Royal Horticultural Society, here .
gardening.stackexchange.com/users/136/Mancuniensis
In this related question , I answered: A handful of compost should be about the consistency of a damp sponge.
What I do is add water when I turn the pile: I turn the hose on a little bit, set it in the spot where the pile is going to be, and start shoveling material onto it.
After a couple of inches of depth, I raise the hose, so the water trickles into the center of the pile.
Then shovel some more, repeatedly lifting the hose every couple inches of depth.
This way, the whole height of the pile gets some moisture.
If it has been hot, and we haven't had any rain, I'll also dump waste water onto the pile.
(E.g. soiled water from animal buckets.)
gardening.stackexchange.com/users/51/bstpierre
Below are a few more sites that contain a lot of good composting information that you may find helpful/useful: Composting Council of Canada At Home With Compost : Clues on Composting
The composter contents should be moist like a wrung-out sponge.
If the contents are too dry, it will take overly long to compost; and if too wet, the contents may begin to smell.
Troubleshooting
If the pile does not decrease in size or generate heat, composting may need a boost.
If the pile is dry, add water - mixing thoroughly.
If the pile is wet and muddy, spread it in the sun and add dry material.
Remember to save "old" compost to mix with incoming material.
Create Your Own Compost Pile
Having the right amount of greens, browns, and water is important for compost development.
Ideally, your compost pile should have an equal amount of browns to greens and alternate layers of organic materials of different-size particles.
The brown materials provide carbon for your compost and the green materials provide nitrogen, while the water provides moisture to help breakdown the organic matter.
Backyard Composting Approach One 1 - Select a dry, shady spot near a water source for your compost pile or bin. 3 - Moisten dry materials as they are added.
5 - Optional
: Cover top of compost with a tarp to keep it moist.
Backyard Composting Approach Two 6
- Top with a 3-inch layer of brown materials, adding water until moist.
7
- Turn your compost pile every week or two with a pitchfork to distribute air and moisture.
Move the dry materials from the edges into the middle of the pile.
Continue this practice until the pile does not re-heat much after turning.
Making and Using Compost Location
Because the compost pile may need to be kept moist during dry weather, a convenient source of water should be available.
But don’t locate the pile where water may stand.
Excess moisture in the bottom of the pile can cause the process to stop or lead to odor problems.
Layering Lightly water each layer as it is added.
The entire pile should be as wet as a well-wrung sponge.
Achieving this result is easier if you water each layer of dry material while building the pile rather than trying to wet the entire pile after it is built.
Care of the pile Decomposition will occur even if a compost pile is ignored after it has been built, but it will occur at a slower rate.
Adding water to maintain moist conditions and turning the pile to improve aeration will speed the process.
To check the moisture content of the pile, squeeze a handful of compost.
If a few drops of water can be squeezed out, moisture is about right.
If no drops fall, the pile is too dry.
If water trickles out, the pile is too wet.
Cover the pile with plastic or other materials during wet weather to avoid excessive moisture buildup.
Piles may be turned by slicing through them with a spade and turning over each slice.
The main objectives of turning are to aerate the pile and to shift materials from the outside closer to the center, where they may also be heated and decomposed.
Moisten dry spots in the pile by spraying with water during turning.
US Composting Council
gardening.stackexchange.com/users/394/Mike Perry
It is very important to keep water and temperature in balance in a compost heap.
The bacteria need water to assist the decomposition process, but too much water will slow down or stop the process completely.
Water should be added little and often, but only as necessary.
A handy tool for compost is a thin slightly rusty iron rod about 4 feet long.
Shove the rod into the pile using your best rapier thrust technique, and as you do this feel the consistency of the materials it passes through.
Maybe you feel twigs and other hard stuff, maybe it is consistently smooth and open.
Push in as far as it will go and pull it back out, and inspect the surface of the rod for signs of dryness or physical water.
Then put the rod back in and leave it there for half an hour, then withdraw again and feel the temperature of the rusty rod, getting your hands nicely dirty and feeling the quality of the compost it passed through.
If your hands get really smeary dirty the pile is probably too wet already and needs drying out and rebuilding.
If the rod feels cool or only slightly warm then the engine is not running.
Maybe it has finished decomposing, or it's time to rebuild the heap, moisturizing, but not wetting, as required.
Buckets of water are only required if the pile is running really hot and shows a dry rod test.
gardening.stackexchange.com/users/15063/Colin Beckingham
Yes, compost needs water but not too much.
It should have the same amount of dampness as a wrung out sponge.
And it needs to be tilled and turned over every once in a while to keep it aerated; that will help prevent mildew from forming.
gardening.stackexchange.com/users/24895/David Goodson
I have a 1m x 1m x 0.6m compost heap. I was turning the heap yesterday and was surprised to find that most of the heap hadn't really decomposed, and was in fact quite dry.  Should I be regularly adding water to the heap to encourage composting?
Should I add water to my compost heap?
gardening.stackexchange.com
<compost><water>
gardening.stackexchange.com/questions/1088
gardening.stackexchange.com/users/17/Paul Turner
Successful composting depends on moisture. Adding water will speed up the procress. It is important to keep water and temperature in balance to help bacteria. Adding water to maintain moist conditions and turning the pile to improve aeration will speed the process. Add water whenever the heap begins to look a little dry as successful composting depends on moisture. The composter should be moist like a wrung-out sponge. If the contents are too dry, it will take overly long to compost. If it is too wet, the contents may begin to smell. As the compost pile may need to be kept moist during dry weather a nearby water should be available.   It is important to keep water and temperature in balance in a compost heap. Bacteria need water to assist the decomposition process, but too much water slows down the process. completely. Water should be added little and often, but only as necessary.  
Adding water to maintain moist conditions and turning the pile to improve aeration will speed the process. Add water whenever the heap begins to look a little dry as successful composting depends on moisture. The composter should be moist like a wrung-out sponge. If the contents are too dry, it will take overly long to compost. If it is too wet, the contents may begin to smell.   As the compost pile may need to be kept moist during dry weather a nearby water should be available.  It is important to keep water and temperature in balance in a compost heap. Bacteria need water to assist the decomposition process, but too much water slows down the process. completely. Water should be added little and often, but only as necessary.  