Like nchenkin, the most memorable animal I ever encountered was a Jaguar. It was in Los Katios Nationalpark in nw Colombia, where hopefully the transamerican highway will remain interrupted forever!
Corcovado in Costa Rica indeed is a great place to see wildlife. We encountered a Baird's Tapir with a young on the beach, pretty close to nchenkin's Yaguar place. In the forest, I was nearly run over by a White-bearded Peccary. Best observation in this park, however, was an Ocelot.
Other great mammals in south america were Yagourundi (Tatacoa desert in Colombia), Coati (different places in Costa Rica), the rarely seen Olingo (Monteverde, Costa Rica), Andean Fox (Ecuador) and Tamandua (Santa Rosa, Costa Rica).
In Africa, a close female Chimpanzee (Tai NP in Ivorycoast) was my favourite. I also walked into Elephants, Buffalos, Hippos, Hyenas, and a Green Mamba, but most animals were seen from cars in this continent.
A young Tiger in Royal Chitwan NP of Nepal increased my heartbeat considerably. Other great observations in Asia were Gaur and Rhino (both also Chitwan), Asian Black Bear (Dachigam, India and Kaeng Krachan, Thailand), Bharal (near Thorung La, Nepal), Himalayan Thar (Trecking to Annapurna Base Camp), Marco Polo Sheep (ne Kyrgyzstan this summer), and Orang Utan (Gunung Leuser, Sumatra, and 2 sites on Borneo). However, my all time favourite, Snowleopard, has not yet been seen by my eyes.
Europe, in comparison, is a bit lame, what mammals are concerned. Nonetheless, I appreciated Ibex (all over the alps), Badger (Britain and Germany), Moose (Scandinavia and Poland), and all these Foxes, Martens and Weasels.
As I had admitted before, I am a birdwatcher for a longer time than I was a mountaineer