Who Can Baptize?

This is post #6 in a series on Baptism:

1. Baptism Questions - some questions I'd like to sort out
2. What Did Baptism Mean? - a look at how the Greek terms get used and translated in other literature
3. Baptism without Water - a look at baptism references that are not talking about water
4. Baptism and Culture -  It seems Christianity adopted a common custom of the time.
5. The Heart of Baptism - What is at the heart of this ritual 
6. Who Can Baptize? - Do we think Matt 28:18 - 20 is addressed only for the clergy? 
7. When Should Believers Be Baptized - At what age? At what level of maturity? 
8. Baptism With The Holy Spirit - comparing immersion with water and with the Holy Spirit 
9. Baptism Summary Thoughts

I came across a quote from John Calvin on this topic:

It is here also pertinent to observe, that it is improper for private individuals to take upon themselves the administration of baptism; for it, as well as the dispensation of the Supper, is part of the ministerial office. For Christ did not give command to any men or women whatever to baptise, but to those whom he had appointed apostles. And when, in the administration of the Supper, he ordered his disciples to do what they had seen him do (he having done the part of a legitimate dispenser), he doubtless meant that in this they should imitate his example.
(John Calvin, Institutes of the Christian Religion (Bellingham, WA: Logos Research Systems, Inc., 1997). Institutes IV, xv, 20)

Do you agree with John Calvin on this?

Or do you think baptism falls under the responsibility of the priesthood of all believers?

Do you think Matt 28:18 - 20 is addressed only for the clergy?

Then Jesus came to them and said, “All authority in heaven and on earth has been given to me. Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.” (Matt 28:18 - 20 NIV)

When we look at all the examples of baptism in the New Testament, are we confident they were all performed by ordained clergy?

I'd love to hear your thoughts.