I am not a romantic. That is one of the reasons I love horror and sci-fi. I will take monsters and gore over smooches and talk about "feelings" any time. As someone who watched The X-Files obsessively since the very first episode in 1993, I was surprised to discover that I had, sneakily, become a Mulder/Scully shipper. I didn't officially recognize this until Season 10 began, but deep down, I think it had been there the whole time.
The way in which The X-Files handles romance is the way I always want romance handled in genre television: as a secondary or even tertiary plot, behind the monsters, the investigation, the weirdness. The pair even call each other "Mulder" and "Scully," forgoing the traditional first names that most people use when they become intimate. That's because for them, it was and is always about the work.
Viewers don't know exactly when Scully and Mulder finally took their relationship to a physical level, but all signs point to Season 7 (though the love has been there a lot longer). There is no timeline of Mulder and Scully's intimate relationship. There isn't even any consensus over whether Mulder and Scully are or were ever married. (David Duchovny seems to think so; Gillian Anderson is noncommittal; series creator Chris Carter will never, ever tell).
It wasn't until Season 7 that they had their very first on-screen kiss, in the episode titled "Millennium." At the end of the episode, Mulder leans in and gives Scully a tender New Year's kiss, along with the coded message to X-Philes: "The world didn't end." There has been plenty of debate as to whether or not it was actually meant as a romantic kiss, or a "Y2K didn't come to pass; this is what you do on New Year's" thing. Later in the season, we see Scully getting dressed and slipping out of the apartment before a naked Mulder can wake. The Season 7 finale is where Scully finds out she is pregnant, and there is only one man who could be the father: Mulder. (CSM has since thrown a wrench in that theory, but I don't trust anything that comes out of that man's mouth.) It is as Scully introduces Mulder to his son in Season 8 that they engage in an indisputably romantic kiss. The original series ends with them together, and in the X-Files movie that came a few years later, they were definitely a couple, even though there was some estrangement as Season 10 opened.
Actors David Duchovny and Gillian Anderson have amazing chemistry together, and that chemistry translates to a pitch-perfect on-screen relationship. Even if you are against the romance of Mulder and Scully, you cannot deny that the two have a wonderful back-and-forth. The best scenes in The X-Files are always ones in which Mulder and Scully are interacting. Whether they are joking casually, or discussing a case, it is always a joy to watch them interact. It's the little things -- a hug, a sideways smile, playful banter, professional arguments -- that is really where these two shine. Anyone can just jump into bed together. It takes a special kind of chemistry to make it look orgasmic.
I think it is more important to be with someone who you have complete and utter trust in than it is to be with someone who can offer grand gestures of romance. That is the relationship I see with Mulder and Scully. Scully, more so than Mulder, doesn't need big romantic gestures or hand-holding to know the love is there. Regardless of what their romantic entanglement is, I think they both realize that their love for each other will last their lifetimes. I choose to believe that Scully's anxiety about what will happen to them when they get old (that she voices while being spooned by Mulder in "Plus One") is her way of sneakily finding out where he stands on their relationship. It is an uncharacteristically insecure move on Scully's part, but I think it shows that she regrets ending whatever kind of relationship they once had.
Ultimately, it comes down to this: Mulder and Scully are, for lack of a better term, "soul mates." The X-Files isn't about romance. It's about aliens, monsters, and shadowy conspiracies. The show is not driven by romance, and that is what makes the show so good. The lack of answers is what makes the romance so intriguing. Their relationship may be the ultimate X-File.