A lot of Christians say that there is such a thing as guardian angels whom God assigns to people. Is this true? I've heard many people say it has biblical evidence but wasn't sure.
The concept of guardian angels is derived from:
"Are they [angels] not all ministering spirits sent forth to minister for those who will inherit salvation?" (Hebrews 1:14).
"Take heed that you do not despise one of these little ones, for I say to you that in heaven their angels always see the face of My Father who is in heaven" (Matthew 18:10).
However, notice that the full concept of guardian angels are not expressed here. What we find is that angels are serving God's people, but exactly what they do and how they do it is not mentioned. I often wonder if the things we referred to as God's providence -- the strange coincidences that happen that makes things work out for us -- are not at least in part carried out by angels behind the scenes. But I can't prove that is what is being meant in Hebrews 1:18.
Matthew 18:10 is a warning that angels are watching over the little ones and so when evil happens, angels are able to petition God directly on their behalf. Jesus is not saying the angels prevent all harm from happening; otherwise, there would be no need for the warning.
See: Angels for more information.