The parts that Blam refers to are known as the pawls and the ratchet inside the freehub.
Slipping can happen for a number of reasons, including worn ratchet, worn pawls, weak springs, or excessive accumulation of grease & grime within the freehub.
http://dirtmountainbike.com/features/work-freehub-body.html
has a thorough explanation of the different freehub types.
Depending on the hub you have, a repair consists of either cleaning, rebuilding or replacing the freehub.
Some freehubs are rebuildable, others are not and must be replaced as a unit.
That said, it's often possible to extend the life of a non-rebuildable freehub by flushing out the old grease & gunk and regreasing.
The mechanic at your local bike shop can almost certainly take care of this for you.
If you're more of the do-it-yourself type, http://www.parktool.com/blog/repair-help/freehub-service has step-by-step instructions for several different freehub types.
bicycles.stackexchange.com/users/2572/keithmo
Check if chain doesn't slack when coasting.
A similar symptom happened to my bike, the cause was a worn spacer inside the free body had deformed and caused drag between the freewheeling part and the body, causing the cassette to apply forward torque on the chain.
This caused a slack on the upper part of the chain, so when i started pedalling again, i had to first take up the slack.
In this case, lubrication helped only a little and for a short period.
Partial rebuild of the free body resolved the issue (however it was a very old hub an it shortly broke again).
If your bike has a freewheel instead, you can just swap it.
In some cases, dirt and debris can contaminate the lube inside a free body or freewheel, and prevent the pawls from engaging.
In such cases, a rebuild using fresh, clean lube solves the issue.
Some lubricants get sticky with time, forming a goo or paste that also prevents parts from moving freely.
The cure is the same as previous.
bicycles.stackexchange.com/users/2177/Jahaziel
Most likely it is not the pedals clicking in but the hub / freewheel
You have little springs on metal that let it click to coast
but when you pedal they catch.
So if the spring is worn or the metal is worn it may not catch on the first and have to travel to the second (or third).
A quarter pedal is a lot of motion.
This is going to get worse as you have fewer points of contact and they are getting banged on.
I know you are not asking about single speed freewheel
but this is a reference freewheel
The trials freewheel has 72 points of engagement for a faster engagement
The coast / engage can be in the free hub or the free wheel - fix hub and freewheel - free hub and cassette SheldonBrown
You might have a freewheel on the bike
BIG.NINE
40-MD
If so you can just replace the freewheel But most likely you have free hub / cassette
You will see hub used for free hub
so just because the says hub does not mean it is not a freehub
And you will see the term freewheel used for cassette
But if they say cassette they typically mean cassette
I doubt this is chain.
Do you have visual slack in the chain?
A 1/4 turn would be chain drooping half way to the ground and you would have problems with the chain coming off.
bicycles.stackexchange.com/users/7785/paparazzo
Basically, there's 2 mechanism in play so it should be one or the other.
A loose in the chain or a broken freehub.
Check that there is no loose when you cross the chain from smallest platter to smallest cog on the cassette.
If there is, remove chain link to remove loose.
Check that your freehub start pulling the wheel almost as soon as it start turning (forward).
If that's not the case, you should change you rear hub or wheel.
bicycles.stackexchange.com/users/12598/kbenoit
Because you say that this happens when the bike is already in motion , I suspect that what you're experiencing is normal.
In most bicycles, the rear hub has a ratchet mechanism which allows it to freewheel in one direction.
This means that when the bicycle rolls forward under its own momentum (or down hill), the pedals do not move.
Moreover, you can pedal backward even while moving forward.
This also means that in order to feel any resistance, you have to pedal sufficiently fast for the speed at which you are going and the gear that you are in.
If you do not pedal fast enough, it feels as if there is no tension in the chain, because in fact there isn't: the hub is moving faster than you, and freewheeling, and so the chain isn't exerting any torque.
You must pedal faster or switch to a higher gear (if possible).
There is also a chance that the ratchet mechanism in your hub is not working properly, so that indeed there is some looseness.
The way to check this is to stand still with your brakes fully engaged, and try to pedal forward.
There should be almost no slack in your drive train: the pedal should not move forward if the bike is restrained.
If the pedals can rotate forward while your bike is restrained from moving, then have it serviced.
It looks as if your rear cassette hub or freewheel may need to be replaced, or some other problem in the overall drive train.
In other words does the problem reproduce when the bike is not already in motion?
If so: problem.
bicycles.stackexchange.com/users/5088/Kaz
I just got an old 90's bike (like new with same problem) and usually it's the poor grease used in older entry level
Chinese made bikes that dries up and turns into wax that does this.
Of course it could be alot of other things too.
Adding light oil may work, from open side of freewheel hub, lay bike on side add oil and let gravity help it get into freewheel, then ride bike.
Some solvents or WD40 could work better on really bad dried up grease.
You may have to tear hub apart and repack with good grease, if it's not a mechanical issue
it's the lube inside period.
Good luck.
PS As a bicycle messenger in Boston for about 15 years , I coined the saying "
In this business either you break the bike, or the bike breaks YOU!"
Be good.
bicycles.stackexchange.com/users/40922/Boston Jammer
I ride a rather usual Merida hard-tail mountain bike. Recently I've come to notice that when I start pedaling (bike already in motion), it can take up to as much as quarter of a turn for the pedals to  click  and the chain to start pulling the bike again. What could cause this and more importantly, how can this be fixed? Is this merely a problem of chain tension?
Pedaling not connecting right away
bicycles.stackexchange.com
<mountain-bike><shifter>
bicycles.stackexchange.com/questions/22996
bicycles.stackexchange.com/users/10694/Nit
Most likely it is not the pedals clicking in but the hub / freewheel. Depending on the hub you have, a repair consists of either cleaning, rebuilding or replacing the freehub. That said, it's often possible to extend the life of a non-rebuildable freehub by flushing out the old grease & gunk and regreasing.  The mechanic at your local bike shop can almost certainly take care of this for you. This is probably the ratchet failing to connect due to a worn part in the freehub or accumulation of grease and grime. You may need to clean, rebuild or replace the freehub. This can be done yourself or at a bike shop.
This is probably the ratchet failing to connect due to a worn part in the freehub or accumulation of grease and grime. You may need to clean, rebuild or replace the freehub. This can be done yourself or at a bike shop.