Mountaineering in Colorado requires a certain set of gear.  Sure, there are some optional items like a GPS or trekking poles, but there's plenty of gear you should always have. The following list includes most of the gear you will need and a few extras, but it does not cover all equipment required for technical climbing.
 

Main Gear:

Food and water (plenty of water)

Hat

Gloves

Synthetic shirts

Synthetic long underwear

Fleece or Wind-Block jacket

Waterproof shell/jacket

Nylon shorts

Hiking pants

Hiking boots / scrambling shoes

Hiking socks

Watch

Pack (that fits the hike/climb)

Headlamp

Sunglasses

Knife or multi-tool

Water bladder or bottles

Compass

Whistle

Maps

Tape

Matches/lighter

30spf+ sunscreen

TP (in ziploc bag)

Cell phone

Trash Bag (large)

Emergency supplies, including a first aid kit

Climbing helmet

Optional: Trekking poles

Optional: GPS

Optional: Water filter

Optional: Satellite Phone (expensive)

Colder Weather and Snow Climbing:

Waterproof shell

Waterproof pants

Mountaineering boots

Mountain axe

Snowshoes

Crampons

Gaiters (ankle or knee-high)

Winter hat

Balaclava or fleece face mask

Avalanche beacons

Avalanche probe

Shovel

Gear for Overnight Summer Trips:

Tent

Sleeping bag

Sleeping pad

AT / Tele Backcountry (BC) Skiing Gear:

AT skis / bindings

AT boots

Tele skis / bindings

Tele boots

Climbing skins