grumpy old man:
I'm gonna open up the can of mules, too.
Well, there's the specimen described in the original post of this thread, although I must say I find the news story to be a bit dubious in its descriptions, but that's typical. It's a very new find which is always good to take with a grain of skepticism, until further research has been performed.
In 2002, a specimen was discovered in Spain which became known as "Pierolapithecus catalaunicus". Many palentologists believe it's the last common ancestor of humans and the great apes, but there's still some controversy surrounding it because of the location in which it was found, so it's not entirely settled yet, but it certainly seems to be what you're looking for.
It dates to about 13 million years, which matches quite well with the genetic evidence which suggests somewhere between 11 and 20 million years ago.
I hate to simply refer people to Google, but here's a Google search.
"Pierolapithecus catalaunicus site:.edu" - The "site:.edu" restricts results to ".edu" domains, by the way. Very handy when looking up scientific stuff more generally.
Your question on why monkeys still exist today is a good one. It all boils down to a phenomenon known as "speciation". You mention the mule and another example would be the liger, a combination of a tiger and a lion. I like the lion and tiger example better because mules are silly-looking creatures.
Ligers and mules are infertile because their parent breeds have reached a point of speciation. That means that from now on, tigers and lions will evolve in separate directions and so will donkeys and horses. If this point of infertility due to genetic incompatibility were never reached, speciation couldn't occur.
Now, what makes the genetic changes reach a point of genetic incompatibility? The only mechanism I'm aware of is isolation. This has been tested in the lab with fruit flies, by the way.
Let's say that we belong to a species called Booboo. We all live happily together and interbreed like it's 1999. But then... there's an earthquake. Everyone panics. Half of us (Googoos) go north and half of us (Foofoos) go south. The area where we used to live is ruined and each group needs to figure out new ways to live off of their respective lands. Needless to say, different lands have different characteristics, so we evolve in slightly separate ways. Sooner or later we reach the level of genetic incompatibility. At that point, there's no turning back and we are in effect two separate species.
That's the strictest definition of a species; genetic compatibility. If fertilization works at all between two species, the offspring is almost always either infertile or not healthy enough to survive for long, or both. The mule and the liger are perfect examples of speciation in progress.
Keep in mind though, that the word "species" is by no means absolute. To pinpoint what exactly is called a species is an everlasting headache because sometimes species can interbreed even though we should rationally call them different species... a good example would be a dog and a wolf. Their physical characteristics can be quite different, urging us to call them different species, but they can still crossbreed. Same with the tiger and lion, which one would think should be able to interbreed because they look very similar, but they can't.
Wow, enough for now.
I've been debating this for years, by the way, so I could theoretically go on forever.