Overall mountain climbing is not a very dangerous sport. Thousands of people climb one or more of the Colorado 14ers each year with no problems. However, it is also important to point out that people do die each year in the Colorado back country. Death and serious injury can be caused by lightning, exposure to the elements, and falling from rocks and ledges.
While I don't consider climbing a 14,000 foot peak to be putting my life at risk, it is important to understand the risks that are involved. You may encounter a bear or mountain lion but the chance of being attacked by an animal in the Colorado wilderness is much less likely than people in the city would like to believe.
Lightning is a serious risk. Being up above the tree line makes you susceptible to being struck directly by lightning. Lightning kills people each year in Colorado and a direct hit is almost always fatal. The best advice to avoid being caught in a lightning storm is to start early. Thunderstorms roll in in the afternoons. It is best to summit in the morning and be headed down shortly after noon. Also, it is important to keep an eye on the clouds. If a storm is moving in get down. Anytime you see lightning or hear thunder it is important to get down to lower elevation immediately. There is too much risk in standing on top of a 14er in a thunderstorm.
Exposure to the elements takes lives every year too. Usually this happens when someone becomes lost in the wilderness and is forced to spend the night outside. Often day hikers with light jackets get caught out all night without a sleeping bag or jacket warm enough for the freezing night temperatures. Obviously, you can carry a sleeping bag and tent with you on every hike. The key is to know where you are, where you are going, and make sure someone knows where you went if you don't make it out. Bring a map and know how to read it. I always study the map the night before so I know what other mountains are around the one I'm climbing. This gives me the ability to recognize mountain features and keep me headed in the right direction. GPS unit are also very helpful but be sure to have plenty of batteries.
Falls from rocks and ledges. People die every year in the Colorado back country from slipping off rocks. If you are rock climbing know the dangers and bring a rope. If you are hiking, don't climb a rock. Some scrambling is fun but know what you are doing and don't put yourself at risk.
Be smart out there. Don't get yourself into more than you can handle and know when to turn around.