A strut does not fail. The shock inside it does. Also the ball joints and tie rod ends(for the steering) is attached to it and they wear out over time. A strut is basically a metal tube that has a coil spring on top of it and that holds up the car. The shock prevents the car body from bouncing a mile after you hit the depression in the road. Google strut construction image.

Assuming you mean a macpherson strut?

they can fail internally - the shock absorber component has valves and seal that can leak.

They can also fail if the spring breaks, or is shortened (as in amateur 'lowering'), and the vehicle driven over uneven surfaces as that can make the strut 'bottom' and do physical damage to the strut and sometimes the frame.

some just started leaking when they were new, like the cortina.

others suffer normal wear after millions of cycles. still others cant conduct their heat after the fluid bath they are in leaks out. most of them get replaced because there exists a different design thats gas charged or has been made with different valving the customer wants to try. some are replaced because people like bright colors. really if they can accept a jounce and respond with control, allow a 1.5 response, they are within spec and you can spend your money on the actual recommended maintenance you may be neglecting?

They tend to wear out over time. Also if you're driving on bad roads (ie. bumpy, not even) it will cause the strut to compress and uncompress more often then it would under normal use causing it to fail earlier on in its life. Also if you hit a deep pothole or something you can blow one out

USUALLY, THE SEALS BETWEEN THE AIR CHARGED SECTION AND THE SHAFT THAT RIDES IN IT. THE OIL LEAKS OUT AND THE DEVICE FAILS DUE TO THAT AS IT ALL DRIES OUT. NOISY SOME TIMES AND YOU WILL FEEL MORE OF THE ROAD.

Wear (they're only good for about 80K miles). Impact, Excessive tire pressure causes rapid wear.

Driving. Rougher roads will cause more cycles and faster wear.