It may never be possible to create
The first time I heard about it I almost couldn't believe it. A sauropod with sails on its neck? It might sound like a fantasy cooked up by an over-imaginative paleontologist, but the early Cretaceous sauropod Amargasaurus really did have two parallel rows of long spines on its neck. The question is whether these spines were "naked" or carried sails, and something that is difficult to figure out without seeing the living animal.
This is a "new" dinosaur, having been described only in October of 2008, but it is one of the most bizarre. It was a small, feathered theropod with a set of teeth organized into a scoop, and four long feathers sticking out of its stumpy tail. As strange as it was, though, it may be one of the dinosaurs most closely related to birds, and has the potential to shake up current hypotheses about bird evolution.
Gorgosaurus might not be as strange as the previous two dinosaurs, but I do have a soft spot in my heart for it. One of the first dinosaur skeletons I ever saw was the Gorgosaurus mount at the American Museum of Natural History, and this tyrannosaurid has been a favorite of mine ever since. It might not be as famous as its cousin Tyrannosaurus, but it was a much sleeker animal. It would probably be best to view this one from a distance, though.
I know this list is getting a little theropod-heavy, but it is hard to resist Baryonyx. At the time it was discovered it represented a new kind of predatory dinosaur with heavy forelimb claws and a crocodile-like snout. Its relative Spinosaurus was discovered first, but it was only when Baryonyx was found that some previously enigmatic theropod fossils began to make sense. Given that it was probably a fish-eater, it might be a little safer to observe, too.
Horned dinosaurs were my favorites when I was a kid, and none seemed as odd as Pachyrhinosaurus. With the huge flattened bosses of bone, it stood out against more familiar forms like Triceratops, and there seemed to be a vigorous debate over whether it had a huge nose horn or a more flattened nose ornament. It seems that the latter hypothesis is more likely, but it still would have been an impressive creature to see!
There are plenty of other dinosaurs I would like to see, but these five are among my favortes. What are yours?