*Note: I suppose I could have included HD-DVD and Blu-ray in the title, too, but come on!
Anyhow, I was just curious. If you have kids still living with you, what do they keep stocked for their viewing pleasure?
And no, I’m not encouraging you or giving you an excuse to go snooping 
For my 6 and 3 year olds: Little Einsteins are the newest craze. It’s great at teaching musical terminology, and highlights one musical composition and one artwork per episode. They also love the Magic School Bus series. Any tv series that has a theme song sung by Little Richard is okay with me.
They own their very own copy of Yellow Submarine, which is apparently no longer produced (I bought theirs on ebay), which they love. Last night my 3 year old put on a Beatles CD and rocked out to Sgt Pepper’s Lonely Hearts Club Band when he should have been sleeping. They also love My Neighbor Totoro and Cars.
If you (or they) like Dr. Seuss and the Muppets, I highly recommend the Wubbulous World of Dr. Seuss, done by Jim Henson Television. Fun show.
For incredibly poor production quality and horrible acting, but excellence in dishing out the Straight Dope, check out the DVDs with Hard Hat Harry, the magical genie with the hard hat. The movies are really pretty cheesy, but I like them and the kids love them. Hard Hat Harry teaches about space exploration, farming, ships (including explaining how exactly it is that a ship floats), motorcycles, etc. The stories all develop the same way: Harry meets 2 kids (one boy, one girl) who are terrible actors, but very enthusiastic. He uses his magical powers, aided with very bad jump cuts, to transport them to places where they learn interesting and useful things. Then he brings them back to where they started and they all go off, happily discussing space or combines, while the cheesy music, written for especially for each episode plays cheerfully on. I can still sing the song for Farm Equipment.
Oh, and if they like animals, they can’t go wrong with Jack Hanna’s Zoo Life series on VHS, which I think you can only get on ebay these days.
The little one is only two, but she has a ton of Wiggles DVDs. She loves the damn things. We don’t let her watch a lot, but when she does she’s either just standing and watching or jumping and dancing all over the place.
She also likes to watch Noddy and Curious George, but that’s only on PBS. I was going to put a bunch of them on DVD until the DVR died last week.
Fantasia is one of my twins’ favorites, they’ve loved it since they were 2 and still ask for it.
Elmo’s World videos are easy to find at thrift stores. Usually 3 episodes/tape.
Beyond that, I usually borrow things from the library or Blockbuster. It started seeming like a good idea after the 3,985th viewing of Frosty the Snowman (really, what DID he accomplish that caused Jimmy Durante to wax poetic? walk around a little? so what.). “It’s time to take that BACK” is a handy phrase to have.
My child (now age 9) has a freakishly large DVD/Video collection but that’s partially because we used to go without cable and so he watched a lot more videos (it was either that or PBS). His current collection includes some Pokemon movies, the three Bioncle movies, some classics such as the Dark Crystal, Wizard of Oz, Charlotte’s Web, most of the Pixar movies, etc. We have satellite TV now though so much of his ‘screen time’ is taken up by Disney, Cartoon Network & Nickelodeon.
Recently, he asked me if he could watch one of my movies. I asked him what he had and he was holding a “Red Green Show” DVD. Good heavens, I’ve never heard that child laugh so hard at a video. He’s working his way through the collection. 
My older two (ages 11 and 7) aren’t restricted from very much in the way of DVDs, and their dad and I love a lot of “kid” movies, so most of our stuff is shared between us. Harry Potter, Labyrinth, Dark Crystal, that sort of thing. Our daughter tends to watch girly tween crap like Hannah Montana and Bratz and Barbie, so those are obviously just for her. Older son likes cool action stuff. Ninja Turtles, Thundercats, all the superhero movies. Youngest (age 3 next month) has the largest individual collection out of all of us. Dora/Diego, Blue’s Clues, Sesame Street. As for “non-kid” movies, the older ones love Monty Python, Simpsons, Romancing the Stone, LOTR, and anime. (Seven year old is a big fan of Akira, which freaked out his gran when she walked in just as Tetsuo started his “change.”)
We don’t have a lot, but here’s what we have.
3 Disney movies (Cinderella, Mulan, Aladdin)
Muppet Show collection
The Court Jester w/Danny Kaye
The Secret of Roan Inish
3-4 VeggieTales videos (yay free videos!)
Anne of Green Gables, the Sullivan production
My Neighbor Totoro
Kiki’s Delivery Service
Schoolhouse Rock
The Tale of Tsar Saltan, a Russian cartoon from their aunt
The younger one likes Wonder Pets on TV, and we borrow a lot of things from the library.
My three year old has several shelves of tapes (yes vhs), mostly Disney classics and a few Barney and Wiggles and Teletubbies.
But they collect dust now because all that matters in the whole damned world is Thomas the Tank Engine.
Having performed in Gilbert & Sullivan operas for many years, I’ve been serenading my daughter with baritone arias and patter songs since before she was born. During the later months of pregnancy, Kizarvexilla’s mother had noted with no small degree of delight that our unborn child would stop kicking and relax whenever I sang to her – the Pirate King’s song (O, better far to live and die) was her particular favorite. These songs continued to serve as the background music for her infancy and toddler years.
The summer before she started kindergarten, I deemed her mature enough to sit through a live performance without causing undo distraction and brought her to see our production of Iolanthe – a curious little operetta that mixes Arcadian shepherds, fairies, and the House of Lords 
. Kizarvexilla was enchanted. She was even more thrilled when I showed her a video copy of the show…not a recording of our performance, but a professional production. She had a small TV/VCR in her bedroom and watched the Iolanthe tape over and over again. Hungry for more, she moved on to The Pirates of Penzance, the source of her favorite song. Before long, she had confiscated my entire Gilbert & Sullivan video library. Almost four years later, she still hasn’t seen fit to give them up.
Geez, we have a million. Probably 25 to 30 Disney and Pixar movies, a lot of them on VHS (my oldest is 13). Some classic musicals like Oklahoma! The Sound of Music and The Wizard of Oz. Some series I recorded off the air, like Little Bear and, for a brief period, The Brady Bunch. We have Christmas videos of How the Grinch Stole Christmas, The Little Drummer Boy and Frosty the Snowman. We also have about 10 Baby Einstein from when the little one was a baby. I loved them; so soothing!
Our seven-and-a-half-year-old daughter has stopped watching the Elmos, Barneys and TeleTubbies, but we still have them in the cabinet. . . Among the other things (and some of these are ours not hers)
The Wizard of Oz (VHS and DVD)
Snow White
Cinderella
Winnie the Pooh
Shrek, Shrek 2, Shrek 3
Wallace and Gromit
Monsters Inc.
Finding Nemo
The Little Mermaid
The Muppet Movie
The Muppet Show collection
Rankin & Bass Christmas Collection
Mr. Magoo’s A Christmas Carol
a couple of SpongeBob DVDs
a Jimmy Neutron DVD
an early Looney Tunes collection
a Huckelberry Hound/ Yogi Bear/ Jinx the Cat collection
Schoolhouse Rock
and so on
We have most of the Miyazaki movies, and those are what the girls watch most, when they reach for a DVD.