Do you like to figure out puzzles and develop your own strategy, or learn how to solve it from others, and then see how fast you can get?
I enjoy the Bandage Cube. It was a challenge for me to figure out ways to systematically move pieces here and there, then to develop a working strategy for solving it.
The Jing's Pyraminx is one of my favorites. I like the size and feel. I recently added stickers to three of the centers to add to the challenge. Now it isn't solved until the centers are oriented correctly. There are pictures on my blog page.
I like the Rhombic Dodecahedron's size. It is small. I find it interesting to work out solutions for puzzles like this in terms of the puzzle pieces rather than their corresponding cube pieces. For example, start with a 4-sided corner. Get the 4 rectangles that go around it.
The 2x3x3 has amazed me as I tried to find different ways to solve it and figure out which I like the best. Corners First? Edges First? Block Building? Utilizing edge 3-cycles, or only swaps?
I like the FTO. I agree that the Master Pyramorphinx is cool.
For awhile I enjoyed solving the megaminx into different patterns. It was interesting and more challenging. Then for awhile I enjoyed solving it edges first, using setup moves and a commutator to solve all the corners.