If I know a little about them, I find almost any ancient creature interesting.
The early mammals during the reign of the dinosaurs were all varied and compelling in their own right; not all mammals during this time were the size of shrews or limited solely to burrowing or scurrying through the undergrowth. Some were the size of badgers, some lived in the water much like otters and beavers, some were gliders (with membranous wings much like flying squirrels and colugos), and there was even a known monotreme (Steropodon).
The pterosaurs and dinosaurs themselves were fascinating. I was amazed to learn that dinosaurs did not even dominate the scene when they first appeared in the Triassic (I had been under the impression that they had ruled the earth from the onset of the Mesozoic). Instead, dinosaurs were secondary players to the more dominant crocodyliform archosaurs known as crurotarsans, which included phytosaurs, rauisuchians, and aetosaurs, as well as the lineage that would lead to today’s crocodilians. It was only after the Triassic-Jurassic extinction event that the dinosaurs would go on to dominate the ecosystems in which they lived.
Perhaps because I am most familiar with them, my top favourite extinct animals have to be the Pleistocene megafauna, from the saber-toothed Smilodon and Dinofelis (hence my username), to the giant hyraxes and hairy rhinoceroses of northern Eurasia, to the weird and wonderful glyptodonts and toxodons, to the monsters of Australia such as Quinkana and Megalania that would be right at home in Jurassic Park. Many islands in the Pacific had mekosuchine crocodiles which were habitually terrestrial, as well as Meiolania and giant flightless birds fulfilling the niches of mammals elsewhere.
This was the world that we humans evolved in and were shaped most by. We shared the planet with humans who were different enough from us to be separate species. We mastered the use of fire, stone, and wood to carve a place for ourselves within this dangerous, vibrant world. We commemorated the beasts that held significance to us such as the cave lion, woolly mammoth, steppe bison, and Megaloceros through the drawings we left on cave walls, and even left records of observations of behaviour from then, such as rhinos jousting their horns with one another just as their surviving relatives do today.
Closer to home, the Pleistocene Cape of South Africa had a much more extensive coastline than today due to sea levels, with a cooler drier climate promoting more extensive palatable grazing than it is naturally now. This was where the earliest evidence of modern human settlement, as well as the earliest known human drawing, has been found (inhabiting caves 77,000 years ago). In this region, modern African wildlife such as elephants, leopards, ostriches, and so on coexisted with extinct species including long-horned buffalo (Syncerus antiquus), giant Cape horse (Equus capensis), the alcelaphine antelope known as Megalotragus priscus, and apparently a species of wildebeest distinct from the two modern ones.
Honourary mentions as favourites would have to be Thylacosmilus, the phorusrhacids (‘terror birds’), and Livyatan (a macropredatory sperm whale that gave the shark Megalodon a run for its money).