An easy way to boost a squat by, say, 50 pounds is to wrap your knees. However, you're not actually stronger - you're simply able to handle more weight. This can indirectly be beneficial if you're into heavy-duty style training with high weight and low reps--but there's a downside: Your knee joint is not keeping up with the muscular development of the rest of your leg.
The wrap is like a crutch for the knee, making it easier to go through the workout but not exactly developing it. If you take the wrapping-shortcut month after month, your knee joint will remain essentially the same. Then, when you one day try a squat WITHOUT wraps, you're running a serious risk of injury with your muscular power exceeding what your joints can safely handle.
When To Use Wraps
That said, there are times when it is perfectly okay to use wraps. If you've had an elbow injury for example, wearing an elbow warmer is a great idea, as it provides warmth but not the same power-boost as a full-blown wrap. Likewise, when you're trying for one-rep max tests for strength and the like (not recommended, but I know many do these anyway), wraps are an added security measure for stability. However, like with wrist straps, if you choose to use wraps once in a while, you should balance it with non-wrapped training to maintain balance between joint- and muscle strength.
I would suggest that for every workout where you rely on wraps, you should do at least two workouts WITHOUT wraps. The smart thing to do is obviously to time it so that you use the wraps for the heavier, more intense workouts where you need the extra support, and make a point of doing the full movements with strict form for the lighter workouts. Of course "lighter" is a relative term - you should challenge yourself with every workout, and if you use 20% less weights when doing your sets un-wrapped, try to do 30% more reps instead. You get the idea.
What If The Damage Is Already Done?
If the damage is already done, and you have relied on wraps for years, you can ease into the routine by alternating between your usual heavy, wrapped workouts and considerably lighter workouts with a special focus on bringing your joints up to par. For knees in particular, seated leg extensions are a great exercise for putting your knee joints on the fast-track. But like I said - EASE into it.
Be observant and make sure your body can handle the weight before increasing the poundage. Elbows are trickier, but you can most likely do one-arm pushdowns safely (using a handle attached to the upper pulley in a cable-cross machine or the like) while rebuilding your strength.
On a side note, a reader once asked why I told him to always wear a weight lifting belt, but to use wraps sparingly. The answer is that the belt is only a safety measure for your back during overhead presses and heavy lifts (squats, dead lifts, military presses etc,) and doesn't actually make it easier to lift the weight nor steal the workload from the muscle group being worked. Just like wearing a glove won't do anything for a bicep curl, a belt won't help push the bar during a military press.
In this case, it is all about the shoulders and the elbow joints, and they have to work equally much whether you wear a belt or not. Wrapping your elbows, on the other hands, directly takes some stress off them, thus interfering with your natural balance between joint and muscle strength as described earlier. As you can see, there's no harm in wearing a belt, whereas wraps enables and even encourages you to exercise your ego instead of your muscles. The conclusion is simple: Go ahead and use wraps, but save them for when you really need them.