Above, the most important item to carry. My helmet is always tied to my pack until I'm ready to use it above the tree line.
For many years I didn't wear one, but a few close calls with falling rocks finally convinced me.
If you don't bring a helmet, I believe you should not be pursuing this activity.
Gloves - Some kind of tough gloves or open-finger gloves - the rough rocks and sharp edges will hack your fingers and palms when you inevitably stumble.
Gaiters - when you scree ski, no stones will enter your boots; also protects your shins while bushwhacking.
Crampons and an ice ax for snowy conditions.
Rainshell or light repellent plastic jacket - 'tis a very miserable situation to be saturated many miles from your car (learned the hard way).
Heavier jacket or light parka - Even on the warmest days, tie a warm jacket around your waist before you head up. The conditions can change rapidly, and the higher elevations are colder and windier than lower elevations.
Apples - you know that exhausted feeling plodding uphill? Stop and eat an apple. In ten minutes you'll be soaring up the mountain again; amazing fruit, that.
More water - can't stress it enough.
