Richie, Potsie, and Ralph.
Samantha, Darrin, and Tabitha.
Bolt, Mittens, and Rhino.
Inspector Gadget, Penny, and Brain.
Pinky, Elmyra & the Brain from their eponymous spin-off.
Comma, comma, and period. 
Reading, writing, and arithmetic
Atropos, Clotho and Lachesis, the three Fates.
Alecto, Megaera and Tisphone, the Erinyes or Furies.
Urd, Verdandi and Skuld, the three Norns.
A lot of female troikas in mythology.
Tom, Dick and Harry
Hook, line and sinker
Shake, Rattle and Roll
Mrs Whatsit, Mrs Which and Mrs Who
Ready, set, go
The Sanderson sisters - Winifred, Mary & Sarah
Middle schoolers would also likely be familiar with Macbeth and the Three Witches who inspired the above trio.
Bart, Lisa & Maggie Simpson
Venkman, Ray & Egon (at least until Winston joined)
Wynken, Blynken & Nod
Three Wise Monkeys (See no evil, Hear no evil, Speak no evil)
The Sun, the Moon and the Stars
Edward, Jacob and Bella
Stop, Drop and Roll (fire safety)
Many movies are in trilogies, e.g. Back to the Future.
Clark, Lois, and Jimmy.
Me, myself, and I.
If we can name any trio of singers/musicians (Peter, Paul, Mary), can we name any other?
Kingston Trio.
Bacon, Lettuce, and Tomato?
I think most people here have missed this part of the OP:
“Up to young teenagers”.
Things like Brady Bunch, Three’s Company, The Marx Brothers, Happy Days, Bewitched, Kingston Trio… c’mon, you’re kidding, right? I’d say that my 14 year old wouldn’t recognize the majority of this list.
Mario, Luigi, Wario
Paper, Rock, Scissors
Jessie, James, Meowth
Victor, Yuri, Yuri
Mustard, Ketchup, Mayo
Scully, Mike, Boo
Timon, Pumba,Simba
Kevin, Stuart, Bob (minions)
For some of them, why not? The Brady Bunch, Bewitched, Three’s Company, Happy Days, still air regularly in syndication. It’s not as if kids today don’t get a chance to watch them.
Colonel Mustard, in the Billiard Room, with the Candlestick?
I may be doing this wrong.
Mickey, Donald, and Goofy.
Bugs, Daffy, and Elmer. (It’s rabbit season!)
Ghost of Christmas Past, Ghost of Christmas Present, Ghost of Christmas Future.
The three musketeers might be a bit confusing for little kids, given that the protagonist D’Artagnan was not one of the three.
For discussions about adoption, don’t mention Larry, Darryl and Darryl. - YouTube
Niña, Pinta and Santa Maria
That’s what I was thinking. Some of the trios mentioned would have been common knowledge to kids of an earlier generation. Today’s kids—some of them might know about them, but they won’t be part of the general culture.
or their physicians, Dr. Howard, Dr. Fine, Dr. Howard. Or the soldiers, Duck, Dodge, and Hyde. Or the reporters, Press, Press, and Pull.
Others:
Abraham, Martin, and John
IRT, BMT, IND
Benelux
My Three Sons