Not Tetris 2 is a very interesting Tetris spin-off. It is a free, multi-platform game. It is currently available for Windows, Linux, and Mac OS X. It is also an open-source project so you can download the source code and compile it yourself if you want. In Not Tetris 2, the blocks that fall from the top of the screen don't behave like the ones that you are used to playing with. They are influenced by physics in Not Tetris 2. For example, if you drop a block on top of another one hard enough, you will move it, albeit slightly. You can't rotate pieces at will. They will start rotating and you have to calculate when to drop them so that they fit other blocks at the bottom of the screen.
In my first few rounds playing Not Tetris 2, I struggled a bit to make lines. I succeeded eventually, but the board was filled with blocks that didn't fit together. After a while, it is easier to understand when to spin a block and when not.
If you don't like the physics-based mode, you can always choose to play the original Tetris game from the options menu before you start playing.
In short, Not Tetris 2 is a nice Tetris spin-off. It is challenging and original.