There are at least 2 types of U-joint failure, one of them often being the cause of the other. It helps to understand how a U-joint works and what it does.
A U-joint has 4 roller bearings that allow 2 straight shafts to turn/flex while the shafts are not in a straight line with each other. It also keeps the shafts in a proper off angle alignment to each other.
1-One failure (sometimes only subtly and gradually noticeable) is caused by the roller bearings becoming dry (from lack of lube) and/or rusted, causing them to bind and not allow smooth movement/flexing..
A-This causes the 2 shafts to force the movements of the binding bearings, creating a sometimes slight or dramatic vibration that is not at all good for the output bearings of the transmission or the the input shaft bearings of the differential, depending on which U-joint is failing. The rollers in the bearings will eventually crumble/grind themselves into dust, or worse.
B-This is often the beginning of the cause of a second type of failure:
2-Worn/ground up/missing rollers inside the bearings causing the U-joint to become loose and not keep the alignment of the 2 shafts correct creating an off balance/off true vibration.
A-This is also very bad for your transmission and/or rear end. As they continue to wear it can lead to many, many problems including the earlier mentioned bearing stress, broken yokes, dropped driveshaft, etc, etc.
U-joints are some of the most important, yet most overlooked/neglected parts of your driveline and can cause a lot of unseen damage when not kept in good working order. When your driveshaft is out of the car, hold the output shaft/yoke (the part that slips in and out of the transmission) and hold the driveshaft at an angle to it and slowly spin the shaft to notice the mechanics of how it works. This will help you understand why the U-joints are so important and why driveline angles are so critical. The more dramatic the angle, the less smoothly the workings of the U-joint.
Sorry for the long post, I just thought it was important and I hope someone with more knowledge can elaborate on/correct anything I've stated.
HTH
Gene