Tomb of the Popes

Many tombs of the popes are right in the main section of St Peter's Basilica and others are downstairs in the Crypt, which does not need any separate ticket or reservation. This has always been enough Popes for me. The church visit is free and separate from the Vatican Museum (with Sistine Chapel). There's also a Scavi tour that gets you closer to the bones of St. Peter (after they were lost and found a few times), but it requires advance reservation by fax or email and is for a limited numbers of visitors.

The SCAVI tour ends in the tomb of the popes

reservations are needed for the tours of the necropolis. You can find more information here: http://www.scavi.va/content/scavi/en/ufficio-scavi.html

I think maybe you are misunderstanding the tickets available.

The Vatican museum that includes the Sistine Chapel have a cost, you can reserve ahead, or take a private tour.

St. Peter's requires no tickets or cost, you can either stand in line to get in (moves quickly) or you can exit from the Museum tour into St Peter's.

The Crypt below St. Peter's where the vast majority of Popes are interred has no cost, you can enter from a separate line outside, there was an entrance from inside St Peter's, but I cannot vouch for that anymore.

There is also the Scavi tour, you need to request tickets far in advance (maybe no cost?) that takes you into the archaeological ruins under St. Peter's, then to the crypt of St. Peter, that also exits into the Crypt, where you can see the other tombs of the Popes.

It's sort of confusing as even the Vatican mixes up the terms sometimes!

You don't need a ticket to visit St. Peter's: it's free.

The grottoes, which are right under the church, don't cost anything to see either, and are sometimes also called the crypt. 91 popes are entombed here as well as some cardinals and other notables. You can visit this on your own when you go to see the basilica. Here's a pretty good map of that area:

http://stpetersbasilica.info/grottoes.htm

Under that level is the Necropolis, often referred to as the Scavi. This was originally a Roman cemetery near the Circus of Nero, and excavations uncovered both early Christian and non-Christian tombs and decorated mausoleums, including one that many Catholics believe to be that of St. Peter. This area can only be visited with a guided tour, and reservations must be made well in advance. Information is here:

http://www.vatican.va/roman_curia/institutions_connected/uffscavi/documents/rc_ic_uffscavi_doc_gen-information_20090216_en.html

To add to the confusion, there's another Necropolis: Necropolis of the Via Triumphalis. This excavated Roman burial ground is not under the basilica but is nearby. It also requires a tour, and those can be booked through the same website you buy your Vatican Museum tickets and other tours from. There aren't any Popes buried in this one, though.

http://www.museivaticani.va/content/museivaticani/en/collezioni/aree-archeologiche0/necropoli-della-via-triumphalis/necropoli-della-via-triumphalis.html

This map shows you where Nero's circus once was in relationship to the Vatican today, and location of both necropoli.

http://www.museivaticani.va/content/dam/museivaticani/pdf/eventi_novita/iniziative/eventi/2013/MV_8_Via_triumphalis_mappa.pdf

You'll find a few papal tombs scattered here and there amongst other churches in Rome but as Laura said, St Peter's has enough of those for me too!