1) Lex: He lives and dies by his trait. Nullifying all damage and hitstun is a pretty big deal. In fact, I feel part of why he's sub-par is BECAUSE of how good his trait is and the fact that his moveset feels like it was toned down to compensate.
2) Zod: I know he's new and I'll admit I probably don't know much about him, but he feels like he depends on his trait to create mix ups/unblockables or even proper pressure against a lot of characters. Like Lex, he really only feels truly dangerous when trait is out.
3) Green Arrow: This character is more or less unplayable without his trait. He is completely designed around it.
4) Bane: To a certain extent, Bane is also designed around his trait. Adding free super armor and damage to his moves is a big deal, and helps Bane get in and beat other characters' tools. This trait was deemed so good in fact that it's one of two traits with a downside, along with Deathstroke (For some reason... maybe Deathstroke's trait is better than people assume? IDK, I don't play him.)
5) Sinestro: This guy becomes a completely different character when his trait is out. Everything becomes safe, combos are extended, and basically you use it as a Marvel assist. A large part of Sinestro's gameplan in most matchups involves getting trait up and running.
To be honest though, it's hard to make a 5 character list considering how useful most traits in the game are.
Raven's trait immediately changes a match. Aquaman gets a Out-of-jail-free card. Batman can follow them in for an easy in or use them to effectively zone. Hawkgirl's trait allows her to do some dirty oki traps, zone out of many characters' typical attack ranges, and generally play in a vastly different way than other characters. The list goes on and on.