I just hate lists like this especially when I think first-timers might see it and ignore something that they may enjoy. I always tell first-timers with kids to spend an extra $20 and buy Birnbaum's Walt Disney World for Kids which is a brilliant way to get families excited about going and gives me insight into what they are most interested in. I encourage them to read it together and have their children mark / score items that get them excited. Then, if they want, I give them a little itinerary based on their markings, along with their fastpasses and dinner reservations, on how to go about each park (go left, always go left).
That said:
1) Stitch - awe come on you have to experience chili dog burp in your face at least once (well, not now it's closed)
2) Carousel of Progress - my mother wants to slap the person that put this on their list. I might hold them for her.
3) Prince Charming Carousel - young kids, or end of night, this ride can easily take you back to childhood if the line is short.
4) Primeval Whirl - it's always good for a smile as you get whipped into that one corner that spins you around the most.
5) Swiss Family Treehouse - see it, enjoy the detail, walk down the stairs and get on the Jungle Cruise for a laugh.
6) Journey Into Imagination with Figment - umm... ride it once and I'll show you video of how great it used to be.
7) Magic Carpets - believe it or not I've never ridden this once. For some reason I'm always sent to get Dole Whips while my wife takes the grandkids on it.
8) Gran Fiesta Tour - A perfect way to let those tequila shots settle you just did at La Cava del Tequila before moving on to get some Carlsberg.
Things we normally don't do much any longer unless we are tired and there is no line:
Magic Kingdom
- Tom Sawyer Island - which makes me sad. This place needs love and is a childhood favorite running ahead and scaring everyone in the caves.
- Liberty Belle - it just takes so long waiting to board (or is that bored?)
Hollywood Studios
- Disney Jr Live on Stage - honestly, the wife does this with the youngest one's while I ride ToT or RnR.
- Beauty & The Beast Show - see above answer.
EPCOT
Animal Kingdom
- Finding Nemo the Musical - haven't done this in a long time, maybe we should again next time we go.
- Kali River Rapids - we go a lot in December. When it's warm enough we ride.
Disney Springs
Who ever thought people want to do high-end shopping while on a vacation at Disney? I get lost in that place now. Bring back the Adventurer's Club and get off my lawn, harumph!