This sounds more complicated than it is, trust me!
Most fluids are Newtonian. That is, as you push or move through them, the more they become apparently more viscous, or push back. Air works similarly to this concept. The Bugatti Veyron, one of the fastest production cars in terms of top speed, needed the extra 500 hp (from 501 to 1001) to go the last 50 or so MPH up to 250. The air at that speed is extremely thick, so the vehicle needed to be extremely aerodynamic, plus have a lot more hp. Water works in a similar way. Moving faster in water requires more and more force as the speed increases.
Non-Newtonian fluids, however, are much more interesting. These do not obey the same rules. Some of them get much harder to 'move in' than others as speed increases, others do the opposite.
An interesting one is a shear thickening fluid. One example is a common physics trick that some of you may have seen. Corn starch in water if mixed to the correct proportions will exhibit solid-like behaviors if put under enough stress (i.e. pressure/force on it). It is possible to run across a pool of it, like running on water. Another example of this is used sometimes in car suspensions. At low stress, the fluid yields somewhat, and at high stress, it yields slightly more, providing a much smoother ride than conventional stiff springs.
There are also fluids that do the opposite, and become easier to move with increased force. The easiest example of this is paint. Applying force against the wall you are painting makes the paint more easily come off. However, when it is on the wall, little force is being applied and it is less likely to move.
The last kind I want to talk about is pretty cool and everyone is familiar with it but likely doesn't realize it. Bingham plastic fluids require an initial force or stress to get moving, but otherwise will not. It's a similar concept to a block of wood on a wedge. At some angle (where the force of gravity is acting more and more readily) the block will begin to slide. I'm not going to talk about the differences in types of friction because that's irrelevant to this, but the idea of it beginning to slide due to a minimum force applied is the idea. Toothpaste is a great example of this. You can hold it upside down and it won't come out. This isn't due to a magical inside vacuum pressure system, it is the fluid properties itself!
Hope you guys enjoyed :)
edit: here is a video demonstrating a shear thickening fluid: