The puma, a.k.a. the mountain lion, may be the most athletic jumper of all the wild and domestic cats. Sport hunters, who’ve obviously had first-hand experiences in chasing pumas, say that this athletic wild cat has an amazing ability to leap 20 feet straight up a cliff and when chased by dogs the puma can make downhill leaps 30 and 40 feet long (source: Wild Cats of the World page 254).
In California the puma has been seen leaping boulders and dodging clumps of vegetation while chasing jackrabbits.
The puma has a relatively long spinal column. This allows for an increased lumbar flexion while running which is a characteristic that it shares with the cheetah. We know how quick the cheetah is. Although the cheetah chases prey down while the puma ambushes prey in classic feline style.
The Puma has powerful and relatively hind legs allowing the animal to attain high speeds in short distances. It is believed that they are adapted for jumping (source: Gonyea WJ 1976 – Adaptive differences in the body proportions of large felids). One puma was recorded overtaking and killing a javelina in a 200-meter chase over desert terrain which it seemingly ignored (source: Van Pelt AF 1977 in A mountain lion kill in southeast Texas). Javelinas can run at 35 miles an hour. My guess is that the puma can run up to 50 miles an hour as a maximum in very short bursts. Occasionally they can catch the fast pronghorn (source: Ockenfels RA 1994 Mountain lion predation on pronghorn in central Arizona).
Some people ask whether the puma can jump a six-foot high wire fence. The only information that I have on that is from one account (visual record) which ‘describes a female puma sitting near her kill, leaping over a two-meter-high mesquite bush and catching a vulture in midair as it was about to land on the shrub’ (source: Wild Cats of the World). Two meters is 6.5 feet. Therefore, the answer to the question is probably yes under the correct circumstances and depending upon the individual animal.
One website says that pumas have been seen to leap 40-45 feet horizontally and 18 feet vertically. Wikipedia states that they can jump 18 feet (5 meters) vertically and up to 45 feet (14 meters) horizontally (Source AZ Animals). Some of this information is circulating on the internet. My information comes from books and hard references.
My impression is that the puma is the greatest jumper of all the cats on the planet. There are a couple of other contenders however: the caracal which probably has the highest jump of all the cats on average or consistently and the serval which can also jump incredibly high from a standing start.
Note: all sources are from Wild Cats of the World. by Mel and Fiona Sunquist. The quote is theirs.