The leads, Jean (Judi Dench) and Lionel (Geoffrey Palmer) are also wonderful. The attraction, romantic tension, and companionable ease (as well as the silly arguments) are entirely believable.
The odd thing is, the other couples aren't as believable. Fans will be upset (I know this since I had an argument about it once with another fan) but I never really bought into the Alistair-Judy relationship. Harry & Sandy were better, but even there, I thought she was a tad too sophisticated (though loaded with commonsense) for the relationship to entirely work. A sophisticated woman can marry a sports guy, but a sophisticated woman who wants glamor and evenings-out...and Sandy does...
The issue isn't as bad as on other shows. I blame the problems with The Mentalist on Simon Baker, who is one of my all-time favorite actors and high on my list of incredibly sexy men--but he tends to play men who are so entirely reserved and damaged and drawn in on themselves, it's hard to see any relationship with his characters working.
With As Time Goes By, the issue isn't as thoroughly irritating as Ross and Rachel. And it's not as "no, sorry, I still don't see it" as Frasier and the last girlfriend in the final episode (I would have linked Frasier with "Put your brother on the phone" Lana Lynley).
But then, in As Time Goes By, the lack of romantic tension between the other couples doesn't matter. The couples all get married eventually, but they stay single for most of the seasons and unlike Niles and Daphne, who are fantastic together, they don't really need to get together. The show is about Jean and Lionel. Everyone else is fodder, however hilarious.