Here is a list of necessary gear needed for hiking mountains. This list is intended for day hikes during the summer months. This is the stuff I generally wouldn't leave without. You can always bring more but I try to keep my pack weight to a minimum. I try to only carry what I will need without putting myself at risk if something doesn't quite go as planned.
1. Map, compass, and/or GPS
2. Sunscreen, sunglasses, and sun hat.
3. Sturdy yet comfortable hiking shoes with a good sock
4. A wind breaker
5. A rain jacket and maybe rain pants
6. Winter hat and gloves
7. Plenty of Water
8. Extra food
9. Hiking Poles
10. Layers (T-shirt, long sleeve shirts, fleece, shell)
11. First Aid Kit
Remember that you are entering a high alpine environment. You should be ready for high winds, rain, and lots of sunshine. The weather changes quickly and you will need layers to stay comfortable. Sunscreen and sunglasses are a must, you will get burned. Don't underestimate the amount of water you will need. Be smart, be safe, and have fun.