The custom developed of visiting seven churches. Why seven? This is probably a confusion with another custom, that of visiting the seven pilgrimage churches of Rome when on pilgrimage there. The visiting of these seven churches was often associated with a plenary indulgence.
There may have been an indulgence associated with the Holy Thursday custom of visiting churches, but there is no more. Rather, the Church offers a plenary indulgence for the following in Holy Thursday:
A plenary indulgence is granted [under the normal conditions] for the faithful who piously recite the versus of the Tantum ergo after the Mass of the Lord's Supper on Holy Thursday during the solemn reposition of the Most Blessed Sacrament.
Here were the seven churches I visited this Holy Thursday here in Rome:
The Basilica San ClementeThis is, of course, the church where I live. We used the Chapel to St. Cyril as the place for the altar of repose. A beautiful setting, I think.
The Church of the Navicella, also knowns as Santa Maria in Domnica
I like this church because of its association with St. Lawrence the martyr. It was on this spot where St. Lawrence used to disperse funds and food to the poor. Our Basilica is not a parish church, so this is technically our parish church.
Santi Giovanni e Paolo (Sts. John and Paul)
When a Bishop is made a Cardinal, he is given as a "Titular Church" one of the Churches in Rome. This church was historically given to the Cardinals from New York City. As you can see below, it is currently the titular church of the Archbishop Emeritus of the Archdiocese of New York, Edward Cardinal Egan. The New York tie is still there, as the chandeliers in the church were all taken from the Waldorf Hotel in New York.
The coat of arms of Cardinal Egan:
Baptistery Chapel of St. John Lateran
Traditionally, in the ancient Church the baptistery was usually placed outside of the church. That is because as a non-baptized, you were not permitted entry into the holy place, because being non-baptized, you were not holy. Here we see the ancient understanding of 'holy' not merely as a euphemism for being morally upright, but as the action of God in one's life. Only after baptism were you able to enter the Church--both literally and figuratively--and participate in the mysteries (i.e., the Sacraments).
Here's a panorama of the baptistery at the Lateran:
Cathedral of St. John Lateran
The Cathedral Church of the city of Rome, and my favorite of all of the altars of repose I saw:
St. Anthony of Padua
This church is just up the street from us, and is run by the Capuchin friars. It is a very devotional and very Italian arrangement. I am just sorry the picture is so blurry.