Miles O'Brien: Ends up transferring to DS9 after accepting a posting as Chief Operations Officer for the station. His wife, Keiko, and daughter, Molly, follow him and live on DS9 as well. Appears in multiple seasons of DS9.
Lt. Cmdr Worf: Transferred to DS9 to Command Division following destruction of the Enterprise-D (Star Trek: Generations film). Eventually accepted position as Federation ambassador to Qo'nos. Appears in multiple seasons of DS9, as well as multiple TNG-era films.
Wesley Crusher: after resigning his commission with Starfleet, he opts to live on Dorvan V to learn from "The Traveler" to journey to other planes of existence. Appears very briefly in Star Trek: Nemesis in a Starfleet uniform, at the wedding. (A cut scene includes dialog with Picard.)
Dr. Beverly Crusher: Serves as Chief Medical Officer on Enterprise-E under the command of Cpt. Jean Luc Picard. Does not appear on any other Star Trek series, but does appear in the TNG-era films.
Cpt. Jean Luc Picard: Appears on DS9 a few times in the beginning season. Still in command of Enterprise-E after the loss of the D vessel (Star Trek: Generations), and appears in all TNG-era films. Name is mentioned during Voyager.
Lt. Cmdr. Data: Did not appear on DS9, although did interact with Dr. Julian Bashir from DS9 while Enterprise-D was in orbit of the station during a TNG episode. Appears in all TNG-era films.
Killed while in service aboard Enterprise-E, by sending Picard back from the exploding Reman vessel instead of himself, sacrificing his life and ending his career.
Lt. Cmdr. Geordi La Forge: Serves aboard Enterprise-E as Chief Engineer. Does appear in Star Trek: Voyager in command of his own vessel in an alternate future timeline. Also appears in the TNG-era films.
Cmdr. William Riker: Continued to serve as First Officer to Cpt. Jean Luc Picard even during DS9 until after the events of Star Trek: Nemesis. Eventually leaves the Enterprise-E to command the USS Titan as Captain. Appears in the TNG-era films, in Enterprise (holodeck episodes) and once on Voyager (thanks to Q).
Guinan: Serves as bartender in Ten-Forward on Enterprise-D. Does not appear in any other Star Trek series, except the TNG-era film Generations. Not clear what Guinan does after the D is destroyed.
Cmdr. Deanna Troi: Continues service aboard Enterprise-E as Ship's Counselor. Appears in the TNG-era films. Appears in Voyager and in Enterprise (holodeck episodes). Eventually marries Cpt. William Riker and follows him to the Titan where they have a child.
Related Characters
Q: Included due to his multiple appearances across multiple series. Q appears quite frequently in TNG, Voyager, and DS9. Spreading his mischief and exploring what it means to be a "petulant" human from a Q's perspective, Q simply IS. Even after TNG, he IS. Period.
Thomas Riker: Created by a freak transporter accident years before Will Riker's posting on the Enterprise-D, Thomas Riker eventually resigns his Starfleet commission and enters into rebellious alliance with the Maquis. He appears in DS9 during the episode "Defiant", where he surrenders his Maquis ship and crew, spending the rest of his life (presumably) in a Cardassian labor camp.
Lt. Reginald Barclay: Serves aboard USS Enterprise-D and E. Eventually transferred back to Earth to San Francisco to work on the Pathfinder Project.
Ends up contributing majorly to opening communications to Voyager in the Delta Quadrant and helping them get back to Earth.