Lockergnome has a link (that appears to be slashdotted) pointing to the “100 oldest currently extant domain names” and lists the oldest 15.
03/15/1985 SYMBOLICS.COM
04/24/1985 BBN.COM
05/24/1985 THINK.COM
07/11/1985 MCC.COM
09/30/1985 DEC.COM
11/07/1985 NORTHROP.COM
01/09/1986 XEROX.COM
01/17/1986 SRI.COM
03/03/1986 HP.COM
03/05/1986 BELLCORE.COM
03/19/1986 IBM.COM
03/19/1986 SUN.COM
03/25/1986 INTEL.COM
03/25/1986 TI.COM
Unfortunately, that list is wrong. That might be the 15 oldest .coms, but cmu.edu (Carnegie Mellon) was registered on 4/24/1985, mit.edu (MIT) was registered on 5/23/1985, and Harvard, UC Berkeley, and Stanford were also registered in 1985 (as I’m sure a bunch others were). I’d actually like to see the real list.