Any vehicle equipped with them and lasting beyond its expected factory lifespan will require strut replacement. This is most modern vehicles today, especially sedans, hatchbacks, and minivans. Many crossover-SUVs also have struts instead of traditional leaf or coil springs.
Struts are basically shock absorbers and coil springs built into one unit. Some vehicles with struts also have separate shock absorbers, especially if the vehicle is larger or build for light- or medium-duty offroad. Some struts are build to have separate shock absorbers fitted inside them, allowing the shocks to be replaced without replacing the entire strut. It's all a matter of design and manufacturer specification.
Eventually, though, the strut will require replacement. Many vehicles will even have an expected interval for this, listed in the owner's manual.
Struts should be replaced in pairs, so either both front or both rear should be replaced simultaneously. All four can be replaced at once as well, of course. If the struts are out of alignment (one is newer than another), it's likely that this will cause premature failure of one or both struts on the axle.
When the vehicle's struts are ready for replacement, there will be a lot of bounce and roll to the car when driving and turning corners. Steering play and a likely squeak or "bottoming out" on heavier bumps will also be noted as symptoms of worn struts.
Replacement is relatively easy. On both the front and rear axles, lifting the vehicle properly (and safely) and removing the tires and wheels gets the job started.
On the rear axle, on most front-wheel drive vehicles, simply removing the bolts that hold the strut in place and then reassembling with the new strut completes the job. Rear-drive vehicles may require that the axle be removed or supported for the strut to be removed. Most will not.
Front struts, no matter the vehicle's drivetrain, will require more work to replace and likely a professional mechanic for an alignment afterward. Most vehicles have the strut connected to the sway arm and steering knuckle or the outer sway bar. This changes the steering alignment when the strut is removed and replaced, requiring re-alignment afterward. Supporting the front knuckle on a stand or brace will keep the knuckle from "falling" and stretching the CV joint or pulling the axle out of its socket.
In all cases, on all four wheels, be wary of brake lines and other items that may attach to the strut for support and carefully unclip and replace them when changing out the strut. Replacing the old strut support bolts with new ones (usually included in the strut replacement kit) is recommended. Be sure to follow torque specifications for those bolts as well.
Note that struts are also called "spindles." This usually refers to the front axle's struts, but can refer to any almost universally in mechanic's parlance.