The debate over the existence of guardian angels should probably pivot on the definition of what an angel actually is. The Bible would, of course, be the best source for this determination but the Bible’s language regarding angels has different connotations or complexities.
Some would consider angels mere mortals carrying Godly messages such as prophets, priests, or church leaders (as depicted in the Bible and in modern times). I just recently did some desktop publishing for a nun who called me an "angel" over and over. Does this mean I was transformed into a spiritual being to help her? (I think not). Using this approach, one could be considered "angelic" if one simply carries out the will of God. If this is true, I think one must be operating in or with the Holy Spirit’s assistance, though.
I believe the Bible does speak of spiritual, non-human beings called angels. These angels were created by God for his direct assistance whether as cheribum, seraphim, archangels, or regular messenger angels. In any case, they exist to serve God's needs. Because of this, if we pray that God send comfort to us, He very well might send a guardian angel to aid our spiritual or physical well-being.
[As an "intangible"], the spiritual side of life remains a mystery and so, our complete image of angels is shrouded in incomplete knowledge. Through the Bible's witness, though, we know a few things for certain: 1.) angels exist, 2.) they are subordinate to God, 3.) They can be good or bad, 4.) they are not to be worshiped, 5.) They perform a myriad of tasks.