A violent strike has one of two possible effects. The first is that it breaks your leader and you loose your fly, the second is that it pulls the fly out of the mouth of the fish. Both are undesirable. Try striking more gently, often a slight movement of the rod to the side is all that is required.
With nymphs a quick strike is essential if you are watching the leader move. If you are actually seeing the fish take the fly you will have to delay slightly to enable him to close his mouth. With dries, a longer delay, sometimes in excess of three seconds can be required before the strike can be made. Timing the strike cannot be taught it takes practice. Lots. However, don't despair, plenty of benevolent fish will come along and hook themselves.
There are times when you will get lots of takes with no successful hook-ups. When fishing subsurface try retrieving into the fish. Alternatively you may have to fish smaller flies. If that fails then try thinner leader material. When fishing the surface, smaller flies can do the trick. Also, finer mono. Fishing the flies in, as opposed to on, the surface normally secures more confident takes. Make sure your leader is sunk - if not, then degrease it. Floating leaders spook fish.
It does happen sometimes that the fish appears to take the fly, but what he is actually doing is drowning it with the intention of returning later (typical example; daddy long legs). There is also one other case study; when a fish takes a dry and is moving so quickly he feels the resistance of the other flies and fails to close his mouth. Here you must fish with either less flies, a longer gap between them or cast some slack line into the leader.
If you are missing takes then check your hooks. Often they can break, especially on dams. Get into the routine of checking your hooks every time you degrease your leader. Also check your droppers when fishing more than a single fly. Droppers sometimes tangle around the main leader forming, what is called, a necking loop. This necking loop is the biggest cause of leader breakages (more than wind-knots). Wind-knots are granny knots caused by tailing loops during casting, which are the result of poor casting technique!