In my Ecclesiology class in seminary, I learned that one shouldn’t partake of the bread and wine (or juice) unless they’ve been baptized and confirmed (confirmation class). Granted, some churches do invite anybody who is “in Christ”, some invite all who wish to come to the altar, regardless of whether or not they’ve been baptized, confirmed, or are even confessed believers, and some churches will invite children to partake in order to sort of train them in the sacraments. Personally though, I understand the importance of being “in Christ”, for communion is an act of worship, and not all who were in the upper room joined in the feast, only those who were with Christ and of Christ.
Communion is also connected with Baptism in that at Baptism, we died to our old selves, are born anew, and become new creations in Christ. In the Lord’s Supper, we’re celebrating this new life and rejoicing in Christ’s reign in both the Kingdom, and in our lives.
When I partake, I see it sort of like a renewing of the spirit, fellowship in the community of my brothers and sisters within the Body of Christ, and acknowledgement of Christ’s reign in me. It’s also a moment of reflection and prayer, for during such, we are to be one with each other, just as Christ is one with the Father. Any conflicts we may have with another brother or sister could only be spiritually-dangerous for the believer and his/her fellowship with the rest of the Body, as well as the Head.
For more information on my beliefs about baptism, see these posts: