Quick Answer: Depending on how you're planning to cook the tofu, it does not always need to be pressed. However, if you want to infuse flavors from marinades in the tofu block itself, it is advisable to press it and get rid of the water.
That's the short answer, but let's dive into some of the cooking methods out there and explore the best way to prepare the tofu...
Slicing and Baking
If you're short on time, slicing and baking your tofu is an easy way to prepare it without having to press it.
All you need to do is slice up your block, sprinkle it with your favorite spices and throw it in the oven with some parchment paper.
Keep in mind, if you do use a tofu press you can make it a lot more flavorful with marinades and help it cook quickly.
As someone who owns several of them, you can see my picks for the best tofu press options here.
If you plan on marinating your tofu, then pressing it is a must. If you don't get the water out of the block, then it will be impossible for any marinade that you're using to get into it.
Also, if you're marinades have any sort of oil in them, having too much water in your tofu is going to mean that the oil molecules can't get in.
As I'm sure you already know, oil and water don't mix!
It's nice to press your tofu before making a scramble, but it's not totally necessary. As you crumble the tofu and move it around in the pan, all of the water will begin to evaporate anyway.
If you do remove the water beforehand, just note that the cooking process will be a lot quicker. The tofu will start to crisp up just like scrambled eggs nearly instantly if there isn't any water to evaporate.
If you look at some of the press options linked above, you'll see that some of them allow you to press and drain the water overnight or in the fridge while you're at work. This can be a time saver if you don't want to spend a long time over the stove.
If you aren't scrambling the tofu and want to pan fry it in cubes or slices, then getting the water out is definitely a good idea. If you don't it will take a very long time to get crispy and firm up. It's actually pretty annoying!
Think about it this way: the heat is only being applied to one side of the tofu at a time when it's in the pan. This is a very slow way to evaporate the water in the tofu block compared to crumbled it or putting it on the oven.
Getting rid of the water for deep frying is necessary because you're plunging the tofu into a large vat of oil. If there's too much water, there's going to be a messy reaction of water and oil spewing everywhere!
Just like I mentioned before, water and oil do not mix!
If you are going to go the deep-frying route, then you'll definitely want to make sure your tofu is as dry as possible.
Personally, I never press the tofu before throwing it into a soup. It's going into a big pot of water anyway, so what's the point of removing the water?
You can cook it in any of the water ways before-hand to change the texture (in which case you might want to press it), but otherwise there's not much of a reason.