I loved their friendship on the TV show. It was probably my favorite thing about it and what really hooked me as a viewer. I found their separation in the last episode the saddest, and it nearly ruined the whole series for me.
I heard about the "relaunch" book series and wondered, do they ever meet again? Is there a novel that features them together? I know that Bashir is featured in several of the books. Is there anyone who has replaced O'Brien as his best friend?
Yes, they do meet again, albeit briefly, in the DS9 Relaunch Novel "Star Trek: The Typhon Pact: Raise the Dawn". Please be warned that the following answer is so ridiculously loaded with spoilers that your head may unscrew and fly off around the room.
After the destruction of DS9 and the return of Sisko from the Prophets, Chief O'Brien and his wife Keiko return from their mission to Cardassia and Doctor Julian returns from his mission to survey the Gamma Quadrant. Both are assigned to Bajor (now a member of the Federation) to supervise the installation and management of their new Orbital Control Centre.
Shortly after arriving, Julian's partner, the genetically-enhanced Sarina Douglas (now working as double-agent for Section 31) is accused of destroying the station, something which ultimately turns out to have been the work of rogue Jem'Hadar elements working to undermine the peace agreement put together by the new leader of the Founders, Odo. Due to the situation, they don't really have much time for hijinks before Julian leaves for Bajor to persuade the local authorities (aided by Vedek Kira Nerys) that Sarina didn't kill thousands of people.
Bashir recognized the voice, and he turned toward the speaker. For a moment, he felt incapable of identifying the man because of the context, and because he hadn’t seen him in so long. Finally, he managed to say, “Miles?”
“How are you, Julian?” O’Brien asked, slapping his hands down on Bashir’s shoulders. “Miles!” the doctor repeated. He reached out and the two men hugged. When they stepped back, Bashir asked, “What are you doing here?”
“Say hello to your new chief engineer,” O’Brien said.
“Miles, that’s fantastic,” Bashir said. “That calls for a drink.”
“Quark,” O’Brien said, “I don’t suppose you have any Irish whiskey back there?”
The Ferengi reached down and held up a bottle.
“That’s amazing,” Sarina said.
Quark shrugged. “I knew he was coming three days ago.”
“That’s impossible,” O’Brien said. “I didn’t even know I was coming three days ago.”
“Whatever you say, Chief.” Quark pulled the stopper from the bottle, poured O’Brien his drink, then headed to the other end of the bar.
