Angels are most definitely real, although what they look like, how they appear, what they do exactly, and what defines an angel is often debated. Hollywood has taken many liberties with their depictions of angels. To help decide if angels are real or imaginary, since angels are clearly spiritual beings, the best source to go to is the Bible.
The Bible tells us quite a lot of information about angels, including true stories of individuals who personally encountered angels. Unfortunately, those folks aren't around anymore to interview, plus there are those who belief that the Bible is a fairy tale, making the existence of angels difficult to proof using only the Bible. Fortunately, though, there are actually reputable and honest individuals alive today who have had personal encounters with angels; three of those stories I'll tell below. Personally, between the Bible and the personal experiences of family members, I have not one shred of doubt about the existence of angels.
From the beginning of time as we know it, there have been angels, created by God himself. Angels are mentioned over 250 times in scripture. Angels are both good and bad. According to 2 Corinthians 11:14, "Satan himself masquerades as an angel of light". His demons are fallen angels. There are categories or classes of angels, including seraphim and cherubim, and the archangel or chief angel, named Michael. Angels have many roles. They can be ministering spirits, as the angels who ministered to Christ after his 40 days of temptation in the wilderness, or messengers, like the angel Gabriel who appeared to Mary. Other roles include praising God, especially in Heaven; guiding, as they gave warnings to Joseph; protecting, as they did with Daniel in the Lion's Den. There are angels engaged in battle, fighting against Satan and his angels and evil in general. How many are there? Per Hebrews 12:22, there are "thousands upon thousands of angels". What form do they take? Hebrews 13:2 states "people have entertained angels without knowing it" implying that angels can look like you or me. They can become visible as already mentioned above, or they can be invisible, as they initially were as mentioned in 2 Kings 6:17, until the servant's eyes were opened. Angels were very real then, and they are very real now. What follows are three stories for you, very short versions, that happened over a span of probably 30 years.
My very sane and reputable brother-in-law encountered four angels late one night after being woken up and feeling prompted to get out of bed and go into his living room. He didn't know why, but the urge was so strong he obeyed it. He stood, alone, in semi-darkness, and waited. After a short wait an angel materialized in front of him, facing him. He could see three more angels against a far wall, praying. There is more to the story but he'll have to tell you that himself!
My young niece was rescued by an angel; she told no one until she was an adult. She had strangled, she said, on a piece of string from a blanket or bedsheet that had gotten wrapped around her neck while tossing and turning in her sleep. She was lifted up off the bed and told that it was not her time, and the string was unwrapped from around her neck.
Lastly, three teenaged nephews were riding dirt bikes next to a 20-ft deep irrigation canal in the Okanogan valley and one slipped in with his bike. A man showed up, walked down the slippery bank, picked up the bike from the bottom of the canal with one arm and pulled it all the way out. Then he was gone. No wet footprints; no footprints at all. Amazingly, the dirt bike started with no problems despite being submerged.
There are endless stories like these, of people like you and me encountering angels, that are told in magazines like Guideposts, or on television (remember Touched By An Angel?), or in churches around the country. There are angels all around us; some seen, some not seen, but all very real.
Some may say that angelic encounters are encounters with other spirit beings, or that angels are alien life forms like in the movies, or that they are some force from within the person themselves, or that visions and encounters are the result of an overactive imagination. They may subsequently argue that these stories of personal encounters do not prove that angels are real. However, for families of faith that have prayed for protection and guidance for generations, they are clearly encounters with angels.