Denver is the state capital of Colorado and is also its most populous city. As such, it has the highest crime rate in Colorado too. This is a liberal, diverse and generally quite safe place to visit but, nevertheless, it is a big city in America. There will be pickpockets, there will be people who will try to mug you given the opportunity, you just need to be sensible and safe.
Be aware of your surrounding and who is close to you. Be mindful of where your valuables are and keep them securely on your person. If you have a bag, keep it zipped/clasped shut and crossed over your body so no one can just grab it and run. Stay in a group or in populated busy areas.