What have you noticed about similarities between the warmups of different arts?

Between the majority of martial arts, it appears that there are many joints and muscles that are commonly stretched. There are however, some warm ups that are relevant only to the martial art being practiced. For example, in Judo, it appears that developing abdominal strength is very helpful in applying the techniques correctly. Push ups and stretching the chest and arm muscles are also important. Stretching the calves is, in my opinion, the most important stretch you should do before practicing Judo. Here is an exercise completely relevant to only Judo: Stretching your hips in a clockwise fashion. This is a very good warm up for improving hip throws. And like possum has said, developing wrist flexibility is important in aikido.

I agree with Keyboard Warrior - the warmups are specific to the instructor, not style.

However, the warmups are generally a prelude to what will be covered in class. If you're going to be doing wrist locks, then, warming up the wrists is expected. If you're going to kick, then, you ought to warm up with cardio, then do dynamic stretches. If you're going to do rolls, then, warm up and back stretches are in order.

But I haven't noticed any unique type of stretching done in, say, Taekwondo - and I've been in a myriad schools for 30 years - they're all generally the same - each instructor does them slightly differently - but ostensibly the same things.

I have noticed wrist stretches in Aikido that I've never done in Taekwondo or Hapkido - but I don't have enough experience in Aikido to state that they're specific to only my school, or to Aikido. I just haven't done them in any other style.