E
Short Answer:
Pokemon who have used the Move Tutor for viable moves.
Long Answer:
There are two types of moves that often become inaccessible in new Generations, and therefore are useful for transferring. I've tried to summarize the specific moves to look for.
1 - Old Move Tutor Moves
The first thing to look for is Pokemon with Move Tutor moves.
A specific example I know of is Gengar, which can be tutored Icy Wind in Gen V or Gen VI (ORAS), but cannot get access to it in Gen VII (SM). This also happens in the case of Azumarill with Knock Off.
Popular Gen V move tutor moves include Fire Punch, Thunder Punch, Ice Punch, Iron Head, Icy Wind, Dragon Pulse, Knock Off, Drain Punch, Tailwind, Stealth Rock, Skill Swap. This is not the complete list of Gen V move tutor moves, but ones I recall as being competitive. I had originally included Roost, but it is now a TM instead. Dark Pulse became a TM again in Gen VI.
2 - Obsolete TM
The second type of move to look for are TMs which are no longer TMs, such as Pluck, which was TM88 in Gen V. Both Swanna and Togekiss can learn Pluck from TM in Gen V, and have no access to it in Gen VII.
There aren't many moves that lost TM status, but some may have niche use. Pluck, Ally Switch, Retaliate, Dig, and Telekinesis all were TMs in Gen V, and are not in Gen VII. Defog is another popular move from an HM in Gen IV that still sees use in Gen VII competitive formats.
Bonus - Breeding From Previous Generation
This really isn't going to be comprehensive, as Egg Moves are specific to the the Pokemon, and there isn't a master list to reference. Anyways, some moves can be bred on, but the Pokemon required for breeding aren't in the current generation.
Extra fun is that sometimes Chain Breeding isn't enough, and you need to set that up in the previous generation to get the move you want. And if you checked that link, you'll notice that Bulbapedia does not have a comprehensive list for me to cite, but just two examples.
For example Exeggcute has Power Swap as an egg move, you just need to breed with Seedot or Tangela (who actually needs it from Seedot anyways), who aren't native to Sun or Moon and have to be transferred from a previous generation. Seedot doesn't even learn Power Swap, but needs to get it from Espeon, which you can get in Gen VII.
If you need all cases of where this method is applicable you'll likely need to crawl Bulbapedia yourself. My recommendation is to look for the Pokemon you want to use, and then backtrack all of the moves that you are interested in.