In TNG S3, Ep. 23, "Sarek," Picard mentions having met Sarek "years ago, at his son's wedding." The only thing close to a wedding I remember is "Amok Time," but clearly Picard was not there. Does Sarek have other children or did Spock marry later in life?
Although this seems to have been an intentionally obscure throwaway line in the original show (something for the fans to chew over) in an edition of the TNG Comic from 1990 Trek Editor Robert Greenberger confirmed that Roddenberry was intending for the line to refer to Spock's wedding;
Q. In the episode "Sarek" it was mentioned that Picard was at his son's wedding. Was this referring to Spock?
A. At a recent Los Angeles convention, Gene and others admitted on stage that it was indeed Spock's wedding. Gene's assistant, Richard Arnold, now says that it should not be assumed it was Spock. Until it's clarified in an episode, we'll have to wait to find out.
However, in the TNG Companion, we learn that there was considerable reluctance to mention Spock at all, for fear of overshadowing the new crew which explains why the line was obscured:
Though Sarek’s famous son Spock is later seen to be very much alive (“Unification”/207-208), Behr recalled the battle at the time just to mention the character at all, with caution still in place about dealing with the original series. Picard does say he attended the wedding of “Sarek’s son” as a lieutenant, though again Spock is not specified.
It may interest you to know that we do in fact get to see the wedding in question in the Trek novel "Vulcan's Heart" where Spock gets married to a fellow Starfleet officer; Lieutenant (now Commander) Saavik:
"Commander Saavik and Ambassador Spock, Son of Sarek, were married on the second day of the month of Sharveen at sacred wedding grounds belonging to the family of the groom." Book Blurb
Picard was in attendance and this was the first time he met Sarek.
Finally, it was Picard’s turn to bow with the gallantry that was as much his heritage as the vineyards of Labarre, France. He raised his hand in the split-fingered Vulcan salute he had been practicing for days and recited the Vulcan words of polite goodwill he had memorized
“Welcome to Vulcan,” Spock said.
“Your presence honors us,” Saavik added. Her voice was clear, but held husky resonances that sent the tiniest shiver up Picard’s spine.
Greatly daring, he decided to try one more sentence in High Vulcan, this time to Ambassador Sarek: “We come to serve.”
“Your service honors us,” the ambassador replied.
He said it right!
Move along! The sun was growing fierce, and, what was worse, Picard felt his captain’s eyes burning holes in him from a position by the gateway. Oh, but how he would have loved to speak longer with the legendary ambassador! Perhaps Sarek would consent to answer a question or two; the ambassador had spent a good deal of time teaching at the Vulcan Science Academy and as a special lecturer on Earth.
Captain Manning’s glare grew hotter. Picard moved along.
On a related note, it's worth mentioning that Spock was already kinda sorta married before, but it ended in a kinda sorta divorce. In the TOS episode "Amok Time", we learn that he was bonded to a Vulcanian woman called T'Pring. He describes the arrangement as being somewhat more complicated than human marriages;
UHURA: She's lovely, Mister Spock. Who is she?
SPOCK: She is T'Pring. My wife.
MCCOY: I wonder when his T'Pring arrives.
SPOCK: The marriage party approaches. I hear them.
KIRK: Marriage party? You said T'Pring was your wife.
SPOCK: By our parents' arrangement. A ceremony while we were but seven years of age. Less than a marriage but more than a betrothal. One touches the other in order to feel each other's thoughts. In this way our minds were locked together, so that at the proper time, we would both be drawn to Koon-ut-kal-if-fee.
And at the end of the episode she kicks Spock to the kerb and goes off with another fella.
SPOCK: Stonn. She is yours. After a time, you may find that having is not so pleasing a thing after all as wanting. It is not logical, but it is often true. Spock here. Stand by to beam up. Live long, T'Pau, and prosper.
According to Memory-Alpha's page on Spock:
Picard stated in the episode "Sarek" that, as a lieutenant, he had briefly met with Sarek at the wedding of the latter's son. Episode writer Ira Steven Behr recalled that caution was still in place during early The Next Generation about dealing with characters from The Original Series, thus it was only implied that the son in question was Spock. (Star Trek: The Next Generation Companion)
If it was indeed Spock's wedding, it would have occurred between 2327 and 2333. Since Picard graduated from Starfleet Academy in 2327 and was promoted to lieutenant commander when he was given command of the USS Stargazer in 2333, he was a lieutenant at some point during the intervening time span.
In the novel Vulcan's Heart, it was the wedding of Spock and Saavik, in 2329, and Lt. Picard, not really knowing why he was there, spends most of it in the company of one of the few other Humans in attendance, Leonard McCoy.
According to his page on Memory Alpha, no he is not. He did have a spouse named T'Pring, but it was later annulled and she went on to marry Stonn.
As for Sarek having other children, he has at least 2 sons: Sybok (with a Vulcan princess) and Spock (with Amanda Greyson) However, Sybok died in 2287 and Picard was born in 2305, so chances are, he wasn't talking about him. This being said, the "wedding" if you can call it that, took place in 2267, so there is a bit of a discrepancy in the timeline.
He also has a "Spock Clone" if you choose to count that.