Since Super Mario World took place in a country called Dinosaur Land, there obviously had to be some dinosaurs there. Oddly, though, there really aren’t that many different species to be found. Aside from the Yoshis, the two main types of dinosaurs that show up are Rexes and Dino-Rhinos. The former are obviously based on tyrannosaurs, but they’re much smaller and have apparently useless wings.
Picture from Ribera on DeviantArt
The latter would presumably belong to the infraorder Ceratopsia, although they’re obviously not intended to be biologically accurate. Stomping a Dino-Rhino will result in a smaller Dino-Torch, which can breathe fire.
Another variation on Dino-Rhinos, the Reznors, are also capable of breathing fire. The Reznors are the guardians of the fortresses, filling much the same role that Boom-Boom did in Super Mario Bros. 3, but they don’t really do much other than sit around on rotating platforms and spit fireballs.
How they got up there in the first place is anyone’s guess, although I suppose it could have been Bowser’s doing. King Koopa is the type who likes to set the same basic trap multiple times. Incidentally, when I first learned that the guy from Nine Inch Nails was named Trent Reznor, my thought was that it was like the SMW enemies. It was only later that I realized it was almost certainly the other way ’round, with the dinosaurs being named after a musician just as many of the Koopalings were. There are also the ghostly Eeries, which resemble young Yoshis.
Oddly, considering that it presumably takes place in Dinosaur Land as well, I don’t believe Super Mario World 2: Yoshi’s Island features any dinosaurs other than the Yoshis themselves. Some do appear in later games, however. Mario & Luigi: Superstar Saga has the Blablanadon, an inhabitant of Hoohoo Mountain in the Beanbean Kingdom who becomes a useful ally to the Marios.
While researching the topic on the Mario Wiki, I also found out about Dorrie, a friendly plesiosaur resembling the Loch Ness Monster, who appears in Super Mario 64 and a few other games.
I am aware that pterosaurs and plesiosaurs are not actually dinosaurs, but popular culture tends to group them together anyway. Birdos are also sometimes thought to be dinosaurs, although their appearance is so odd that I’m not sure anyone knows quite what they are.
Evolution seems to have taken some strange turns in the Mushroom World, but I guess they ARE the creatures that managed to adapt to an environment full of floating blocks, flying platforms, mushroom-shaped cliffs, smiling clouds you can walk around on, and holes to nowhere.