I like new, high-tech, components that I can get as free samples by visiting the manufacturer's web site. Sometimes these are only available as itsy bitsy teeny weenie SMDs, so it is problematical whether or not I can actually "play" with them.
For example, I received an assortment of high-performance analog amplifiers (op-amps mostly) from Analog Devices a few years ago and each one was packaged in a plastic box with conducting "foam" inside. The individual device was almost invisible, it was so small! I know I can purchase "adapter boards" to solder these little packages onto, and the adapter board will spread out and extend the device terminals to more accessible solder pads, but I haven't done this yet. The parts remain in their original packaging, getting obsolete by the minute, while I procrastinate. I love analog design, but most of my time of late has been digital. My new Arduino Uno adventure (just starting) offers the opportunity to get involved in mixed-signal (analog and digital) design. And one of these days, I will fire up that Raspberry Pi that has been sitting in my office for two years, gain some familiarity with Linux, and proceed down that road too.
I also like the "almost free" but reasonably priced and fully populated and assembled circuit boards called "reference designs" that most semiconductor manufacturers offer. I have several Texas Instruments MSP430 based reference designs that have built-in USB interfaces for programming. These are more than fun to play with. I might eventually design one into an application eventually, but this will also require a custom PCB and all that entails. Everything is a prototype design for now.
So, bottom line: my favorite component is ALL of them!
