Like others here the three cassowaries are high on the list but also I've found that the giant storks of the genus Leptoptilos are like the modern day Azhdarchids (giant pterosaurs like Quetzalcoatlus, Hatzegopteryx & Arambourgiania) with their massive size in relation to other storks and waders but also their feeding habits. The Azhdarchids were primarily ground dwellers who fed on smaller dinosaurs and carrion like the giant storks. In addition their massive wingspans enabled them to fly for super long distances to find their next food item (think Boeing 747's of the Cretaceous) and the way they got airborn was by launching themselves up in the air like a bat. For more on them, specifically Quetzalcoatlus watch Flying Monsters with David Attenborough. Also, spoonbills have recently made me think of the duck-billed dinosaurs, specifically Edmontosaurus annectens and the Chinese super giant Shantungosaurus giganteus. I really love AMNH's pair of Edmontosaurus (formerly called Trachodon mirabilis when they debuted in 1907) in their Hall of Saurischian Dinosaurs. In addition, when I saw Sarus Cranes up close in Miami for the first time I thought "they're like feathered Struthiomimuses with no tails!"
Terror birds (Phorusrhacidae): (fyi: this bird wasn't godzilla-sized, rather the horses were teeny tiny)
Also, Azhdarchids, which were totally awesome, were actually pterosaurs, a group of flying reptiles that were not dinosaurs
Maribou storks look like dinosaurs. I think most baby songbirds do before their feathers come in completely.