1. This was the first console controller with any analog stick at all.
2. Goldeneye, though it controls differently to modern shooters, was an excellent use of the single stick at the time. You could also use dual sticks by using two controllers at once - groundbreaking!
3. The Z-button was the first trigger-style button on console controllers.
4. The rumble pack was one of (if not) the first force feedback options for console controllers.
So obviously very many of the concepts in the N64 controller laid the groundwork for what became the standard controller design later, with dual triggers, dual sticks, and built-in force feedback.
Personally I think the N64 controller was less weird than:
1. Gamecube controller
2. Wiimote
3. Dual Screen handheld with touchscreen and stylus
4. Probably whatever the Wii-U had.