Pretty well known:
The Spinning Dancer is one of the aforementioned brain tricks that screw with your brain's cognition. you can see it spinning clockwise or counter-clockwise depending on how you look at it, because there's no depth perception with it due to it being a shadow...
... maybe if you stare at it long enough, you'll see it switch...

Also, well-known:
The Checker Shadow Illusion comes from the brain's auto-correction feature, or the brain's need for everything to always make sense. The brain assumes that Point A and Point B are different shades, due to the brain wanting to "finish the pattern" with the combination of the shadow attribute where the brain assumes that the surrounding "checks" are darker, however they are the exact same color...

...it's also worth mentioning that this effect can occur outside of art and in real-life as well... LINK.

There's no image for this next one, and you can try it yourself!
As you may know, the left side of the brain controls things like language, speech, reading, writing, movement, etc. The right side, not much of anything... However because of this, the left side can be "short-circuited" to put it in bad terms, by specific movements. For example,
You can not move your right hand in a counter-clockwise position while moving your right foot in a clockwise position. (Please note, I said "foot" and not leg)

Notice that without moving your foot, you can move your hand in perfect rotation, but with your foot moving it's... not so much. Your brain's attempt at combining both motions into one...

As well as, visual tricks and physical tricks; there's also auditory tricks...

Probably the most famous auditory illusion ever, it's the Shepard's Tone. A tone made of multiple sine waves that confuse our brains. The tones will continually rise (or drop) in pitch, and every so often, one of the tones will drop an octave, but our brains don't notice because the other 2, still rising (or declining), cover for it... Giving the illusion that the tone is endlessly rise/falling.

LINK!

Another auditory illusion:
the Virtual Barbershop utilizes the use of sound channels, to put different effects and sound variances in individual ear canals to make your brain think you're really at a barbershop. However, it's required that you close your eyes and have headphones to work properly...
Has a somewhat eerie feel to it...

LINK!

Lastly, I introduce you to some philosophical questions, that real scientist and psychologists wonder, due to the brains way of adapting...

As you know, it is possible for people to live with just half of their brain, and they still feel consciousness. A common speculation is what would happen if someone was able to put half of your brain in one body and the other half in another body. Which would REALLY be you? Would both of you still share the same consciousness?

LINK!