Your vehicles steering and suspension typically deteriorates slowly over time and can be unnoticeable until you hear that rattle or clunk. The parts that typically fail include ball joints, tie rods, struts, shocks, springs, control arms and stabilizer links or sway bar links.
Ball Joints/Tie Rods:
Imagine yourself holding a baseball tightly, but over time your grip loosens and the baseball falls out. This is similar to how a ball joint and tie rod work. Its a ball in socket joint and they wear out causing looseness and sometimes catastrophic failure where the joint comes out of the socket. Your tie rod is the steering rod between your rack and pinion and the ball joint is the pivot point between your axle/control arm and wheel assembly. The easiest way to spot issues with these parts is abnormal tire wear. That would be a lot of tread on one side of the tire and a little tread on the other side. So something as simple as walking to your car and looking at the wear on your tires can save you some time and money. In worse cases you may experience a clunk or rattle when turning, hitting a bump, or pulling in and out of your driveway.
Your strut and shock are fluid filled reservoirs that when compressed release back slowly. This eliminates what would be your tire bouncing like a basketball and it counter acts the reactive force of the spring in your suspension. The difference between a shock and a strut is that the strut has a spring built into it and the shock is a stand alone part. Usually you will hear a clunk when hitting a bump when your strut fails. Struts and shocks are not a huge safety issue when they fail. Struts and shocks help your tire maintain traction better when they are functioning properly, again eliminating the basketball effect. This gives you better ride comfort but most importantly allows you to brake more effectively because of the added tire to road/surface contact. So replacing your shocks and struts is a safety issue but can be repaired without a catastrophic event.
Stabilizer Links/Sway Bar Links:
These little links are basically rods that connect the strut or suspension to the sway bar or stabilizer bar. Without going into all of the great detail of the Corvair and the issues they had that led to the invention of the sway bar, basically this bar eliminated the "boat feeling" or excess sway and helps stabilize the vehicle. These links have rubber or plastic bushings in them that wear out and need to be replaced over time. This is the most common clunk, rattle or consistent repetitive drum type noise in a vehicle. They tend to rust and break as well from the constant up and down motion cycles they are subjected to.
Some vehicles, mostly bigger trucks have heavier duty suspension so parts like, pitman arms, idler arms and drag links are more common in these applications. With heavier vehicles you need heavier parts and the idler arm and pitman arm serve as pivot points off of the steering gear box which your steering column attaches to and drives. A drag link is an additional tie rod that connects the additional moving parts in this type of system. All should be checked for play or looseness and often times these loose parts can create excess back and forth play in a steering wheel that the drive can feel when driving. Your vehicle may want to wander or the wheel might have extra slop in it. Additional to your suspension, a loose hub bearing or wheel bearing can cause a humming noise and abnormal tire wear as well.
FOR THE DIYer:
To properly check for these issues you should lift the wheel up you are concerned about an inch or two off the ground. Try to allow the suspension to remain unloaded so choose the frame or a pinch point as the lift spot. First grab the sides of the tire and shake it back and forth as if you are trying to turn the wheel. If there is any movement, this can give you an idea that there is play in a tie rod or steering issue (Pitman, idler, drag link as listed above). Once you have done that grab the top and bottom of the wheel and do the same. This can indicate a worn or loose wheel bearing or a really loose ball joint. Lastly put a pipe or pry bar under the wheel as a lever and pull up and down on the end. This will show you the amount of play or looseness in the ball joints. If there is a clunk or excessive movement you should consider replacing the ball joint or control arm assemblies.
Finally the shocks and struts are recommended to be replaced every 50-70k miles. That is a good rule to follow. Most people wait until they hear noise or see fluid leaking from the shocks and struts, but they are a general maintenance item and should be considered if not done by the 100k mile mark.
All in all that gives you a good overview of diagnosing a rattle, clunk or pop. Stay safe out there!