The Shuttle Orbiter crew were obviously in contact with ground control in Houston during their landing, but were they also in contact with any air traffic control, especially once they reached US airspace? Was US ATC involved in the landing in any way other than keeping other traffic out of their way?
Well, sort of. The Kennedy Space Center, where the shuttle operations were conducted, has an ATC. but then, the show was run by NASA, not FAA.
The shuttle operations were coordinated through the Aerospace Control Officer (ACO) at the Air Force 45 th Space Wing’s Eastern Range (it used a military TACAN). FAA was informed of the shuttle landing and nothing else. NASA simply cleared the airspace for a 30 mile radius around the intended landing site to prevent collisions.
In the trajectory of the shuttle landing, FAA issued a NOTAM called 'Space Shuttle Landing Operations Advisory' to warn the users that 25 miles to either side of the nominal reentry trajectory is potentially vulnerable to debris, but the airspace is not closed, like this example:
FDC 9/1945 (A0856/09) - ...SPACE SHUTTLE LANDING OPERATIONS ADVISORY... EFFECTIVE 0911271848 UTC UNTIL 0911271923 UTC SPACE SHUTTLE LANDING OPERATIONS 25 NM EITHER SIDE OF THE LINE BETWEEN 2743S/17214W 0411N/16214W 2925N/13455W 3440N/11828W 3457N/11745W FROM SURFACE TO UNLIMITED. WIE UNTIL UFN. CREATED: 25 NOV 21:11 2009
For these actions, Special Use Airspace was activated. The ACO coordinates these actions with the FAA’s ARTCC (Air Route Traffic Control Center) in Miami, Florida
Pretty sure the K.I.S.S. (Keep It Simple for the Spacemen) principle applies, and NASA owns the airspace. Really, what is Center going to tell the shuttle? "Go around?" Nah. Welcome back? Probably, but that's more a distraction than anything.
ATC would be involved in keeping the airspace clear of other traffic, certainly.
It should also be noted that during at least part of the decent the Shuttle was incapable of radio transmissions. This was a problem common to all space craft reentering the atmosphere. The problem was apparently solved latter in the space program with the TDRS communication platform but the early shuttles were subject to a black out that lasted as long as 30 minutes. Since the US does not have an official definition of the start of space (although they use the generally accepted Karman line) its hard to even say where airspace ends and space begins. There is technically no upper bound to Class E airspace here in the US, the official wording is
(a) The airspace of the United States, including that airspace overlying the waters within 12 nautical miles of the coast of the 48 contiguous states and Alaska, extending upward from 14,500 feet MSL up to, but not including 18,000 feet MSL, and the airspace above FL600
Note: you dont need to contact ATC to enter class E but they will need to pass through the class A at some point.
Also of some interest, you need a valid FAA pilots license with an instrument rating to fly a reentry vehicle.
(c) A pilot and a remote operator must—
(1) Possess and carry an FAA pilot certificate with an instrument rating.
All re-enty and launch paths must be filed with the FAA as well (I assume this is to they can issue the TFR)
(a) Not less than 60 days before each RLV mission conducted under a license, a licensee shall provide the FAA with the following information:
(1) Payload information in accordance with 14 CFR §415.59 of this chapter and §431.57; and
(2) Flight information, including the vehicle, launch site, planned launch and reentry flight path, and intended landing sites including contingency abort sites.
(3) Launch or reentry waivers, approved or pending, from a federal Federal range for at which the launch or reentry will take place, that are unique and may affect public safety.
(b) Not later than 15 days before each licensed RLV mission, a licensee must notify the FAA, in writing, of the time and date of the intended launch and reentry or other landing on Earth of the RLV and may utilize the FAA/U.S. Space Command Launch Notification Form, contained in part 415, Appendix A, of this subchapter for doing so.
(c) A licensee must report a launch accident, launch incident, reentry accident, reentry incident, or other mishap immediately to the FAA Washington Operations Center and provide a written preliminary report in the event of a launch accident, launch incident, reentry accident, or reentry incident, in accordance with the mishap investigation and emergency response plan submitted as part of its license application under §431.45.
Directly to the point the FAA does require a communications plan but seems to specify more what needs to be communicated than mandating they are involved.
(a) An applicant shall submit a plan providing vehicle safety operations personnel communications procedures during the mission. Procedures for effective issuance and communication of safety-critical information during the mission shall include hold/resume, go/no go, contingency abort, if any, and emergency abort commands by vehicle safety operations personnel. The communications plan shall describe the authority of vehicle safety operations personnel, by individual or position title, to issue these commands. The communications plan shall ensure that—
(1) Communication networks are assigned so that personnel identified under this section have direct access to real-time, safety-critical information required for making decisions and issuing commands;
(2) Personnel identified under this section monitor a common intercom channel for safety-critical communications during launch and reentry;
(3) A protocol is established for utilizing defined radio communications terminology; and
(4) Communications affecting the safety of the mission are recorded in a manner that accurately reflects communications made on individual channels, synchronized time coding, and sequence of communications.
(b) An applicant shall submit procedures to ensure that licensee and reentry site personnel, if any, receive a copy of the communications plan required by this section and that the reentry site operator, if any, concurs with the communications plan.
You can find all the FAA regs on space flight here.