Many non-Catholics, in their confused zeal for Jesus, are constantly asking Catholics if we are "born again," admonishing us that unless we are "born again" we cannot be saved. But you see, Catholics, like St. John the Evangelist in the third chapter of his Gospel, relate the phrase "born again" to the results of Baptism. Baptism is how we enter into the New Covenant, in the same way the Hebrews and Israelites entered the Old Covenant through circumcision (which, you'll note, was done to infants).
When many Protestants use the phrase "born again," they seem to be referring to an "emotional experience." They often expect instant transformation (which can certainly happen), speaking in tongues, miracles, etc. as some sort of "proof" of having been "born again."
Catholics most certainly agree that repentance (what we call "metanoia") is necessary and that inner transformation (what we call "theosis" or "sanctification") is the goal, but we are very conscious of not confusing "feelings" with "faith." These are two different things, and mere "feelings" can lie: ask anyone who's ever been "love-bombed" in a cult, experienced cocaine or Ecstasy, been to a Woodstock-like music festival, or is just having a really excellent day. Oceanic "feelings of oneness" and "happiness" can be had in pagan religions (read about Greek and Roman "bachanalias" sometime), through natural or artificial chemicals, through the feeling of "falling in love," through hypnosis, through highly sensual experiences, and other things that have nothing to do, inherently, with Christ. The ancient Greeks babbled in tongues, and glossolalia can is still practiced today among Voudun ("Voodoo") cults, during Japanese seances, and by other false religions and in other cultures all over the world. These sorts of experiences must be discerned, and the spirits must be tested! Remember what Christ said would happen even back in the first century:
For there shall arise false Christs, and false prophets, and shall shew great signs and wonders; insomuch that, if it were possible, they shall deceive the very elect.
It is important to test the spirits and not devalue reason and doctrine! Know that the fruits of the Spirit are love, joy, peace, longsuffering, gentleness, goodness, faith, meekness, and temperance according to Galatians 5:22-23. The fruits of the Spirit are not out of control shaking, screaming, running around, falling down, "holy laughter," vocalizations that don't edify the Church, a "feeling" that doctrine and religion are now unimportant, etc. One should be more in control of one's self after an encounter with the Holy Spirit, not less.
As to "personal relationship with Jesus, " think of the great Saints -- everyone from Thérèse de Lisieux to St. Francis -- are these people not "born again" in the Protestant sense of "having a deep relationship with Christ" while still remaining 100% believers in traditional Catholic doctrine? Read about the life of St. Patrick and then talk to me about a "personal relationship" with Jesus that some Protestants think Catholics just don't understand.
What of our holy martyrs like Maximilian Kolbe or Nikolaus Gross, murdered by Nazis because of the virtue compelled by their Catholic faith? What about Joan of Arc, martyred for her refusal to deny the divine origins of the voices that led her to defeat the English? If you want "personal relationship with Jesus," read the writings of St. Teresa of Avila or St. John of the Cross!