How do we know angels really exist, when we can't see or touch them? I suppose I ought to take it on faith that they exist since the Bible talks about them, but I have a hard time doing that. Or does it really matter? — J.Y.
Yes, it does matter whether or not we believe in the angels—and the reason is because if we do, it will be a source of great comfort to us. The Bible says the angels are "ministering spirits sent to serve those who will inherit salvation" (Hebrews 1:14).
Note that the Bible calls them "spirits"—that is, they are spiritual and not physical beings. That is why the work they carry on is largely unseen and unknown by us—and that's the way God intended it. Only rarely does God give them the power to assume a visible or physical form—although the Bible recounts some occasions when this happened. When Jesus was born, for example, we read that "a great company of the heavenly host appeared" to the shepherds (Luke 2:13).
Angels are not to be worshipped, nor are we to look to them for our salvation. Perhaps one reason their work is largely invisible is so we won't be tempted to place too much emphasis on them, or look to them instead of Christ to save us.
At the same time, if you know Christ, you are never beyond God's love and care—and the angels are a proof of His concern for you. Make sure of your commitment to Christ, and then thank God that He continually watches over you through His angels. And someday in heaven we will realize just how much they did for us, even when we weren't aware of it.