Although many people believe in angels, there are plenty of others (myself included) who can't help but wonder if they truly exist. Angels are messengers of God, whose purpose is to complete certain assignments. Many people who believe in angels have experienced "divine intervention" at times in their lives when they needed help the most, which makes their faith a reality.
A true "angel" is thought to be a perfect creation of God, specifically crafted to feel the purest love and tender care toward all of God's creations. Angels have innate senses of ethics and morals, and angels are inherently wise as well. An angel has a natural understanding of God's will and how God's rules must be applied to other creatures, because this is the way s/he was created.
Angels and their stories are prevalent in many world religions. When a spiritually devoted person prays, it is an angel's job to hear and carry out God's will in God's stead. This can come in the form of physical assistance, but often it is in the form of emotional or intellectual inspiration for the devotee. The person who is in need of help can feel the peace and healing in his or her heart, or will become inspired to find a way out of the problem s/he is contemplating. Angels can help make those connections for people as well.
I, personally, feel that belief in angels can't possibly hurt, and it may even help. I do believe that spirits exist in the physical realm. And my experience with spirits has shown that most entities who have chosen to remain here on Earth are genuinely interested in helping people. Perhaps these are what some people call "angels." One thing is for certain, however; you will not be helped if you don't ask!