As a kid in the early 70's, I was fascinated with all of the recurring elements. The uniforms were awesome...bright colors, black pants that ended below the knees and cool boots. The ship with it's unique shape that looked kick ass from any angle (probably the only Trek ship that can make that claim). Unique looking tech that was sleek and instantly recognizable from the basic shape of the phaser to the flip top action of the communicator. You could draw both in stick form and people knew what it was.
Great sets, especially the bridge, engine room and transporter room. The captains chair. The whole beaming thing. The guy who could kick ass, the guy who was super smart, the guy who could heal anything and the guy who loved those engines. Distinct and incredible use of sound fx, from the bridge to the transporter to the sound cue of the engines to let us know when the ship was kicking into high gear or slowing down.
Beautiful women, strange aliens, crazy machines, ancient civilizations and the occasional time travel. It was serious, it was funny, it had charm. It was a strange self contained world unlike anything else and to my child's mind, that was fucking awesome.
Why do I like it today? Because all that stuff is still cool to me.