There is no indication in the Bible that people have a personal guardian angel who watches over them.
This is not to say that angels have never cared for people and protected them in certain situations. For instance, Shadrach, Meshach and Abednego were hurled into a superheated furnace and yet an angel was there to help them through it. (Daniel 3:25) Daniel was in a lions' pit and survived by means of a protective angel. (Daniel 6:22) The apostle Paul rhetorically asked (yet fully knowing the answer): "Are they [angels] not all spirits for public service, sent forth to minister for those who are going to inherit salvation?" (Hebrews 1:14)
The most notable thing about Hebrews 1:14 pertaining to this thought is that it doesn't indicate the existence of personal guardian angels, but rather that they are "all spirits for public service".
It is also interesting that some angels even refused to give their names to humans. Genesis 32:29; Joshua 5:14; Judges 13:17, 18. It would make sense that if God wanted us to know the names of many angels, he would have revealed these in his Word, the Bible. But by not providing a list of the names of the angels, the Bible safeguards us from giving angels undue honor and worship.
Really, the scriptural view is that we don't have personal guardian angels nor do we need rely upon them, because we have the privilege of prayerfully approaching and relying upon the Creator of the angels, God himself. The scripture says that, "...He is not far off from each one of us." (Acts 17:27)
For more, see:
Do You Have a Guardian Angel?
How Angels Can Help You
What Can Angels Do for You?
Should Christians Expect Divine Protection?
Angels - How do they affect us?
The Truth About Angels
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