What navigation systems were used by the Space Shuttle during reentry?
With the exception of GPS upgrades, I don't believe there were any substantial differences in navigational equipment between the various Space Shuttle Orbiters for most of their operational history.

Each space shuttle had:


3 Inertial Measurement Units
3 TACAN receivers* see GPS Upgrades
4 Barometric Altimeters
3 MSBLS Receivers
2 Radar Altimeters
2 Air Data Probes
Star Tracker (on-orbit)
Rendezvous Radar (on-orbit)


There is lots of information about the Shuttle's navigational equipment in the Shuttle Crew Operations Manual.

GPS Upgrades

In the early 1990s, it appeared that TACANs were going to be phased out, so NASA began evaluating GPS as a possible replacement. Space Shuttle Endeavor was the first to have a single GPS receiver installed in 1993, followed by the other shuttles beginning sometime around 1996.

By 2002, each shuttle had 1 GPS and 3 TACAN receivers. The plan was to remove the TACAN receivers and install two additional GPS receivers - resulting in a 3-string GPS system. However, after the loss of Columbia in 2003, it was decided that the Space Shuttle Program would be discontinued in 2010 (later extended to 2011), and therefore it wasn't worth upgrading all three remaining shuttles. Only Endeavor was upgraded. Discovery and Atlantis continued to fly with 3 TACANs and 1 GPS for the remainder of the program.

You can read a lot more about the history of the GPS system here: Operational Use of GPS Navigation for
Space Shuttle Entry.