Yes, you can observe evolution. I forgot who is doing it and at what college, but they have been breeding and selecting various forms of E. Coli for about 30 to 40 years now.
They started with a very simple strain of E. Coli and they have bred new strains, changed the size and shape, alter how much it can eat and survive.
Darwin also did this with his birds, breeding and selecting various forms of animals.
If you're talking about the observation of the creation of a new species, we have done that too. Africanized killer bees would probably never exist without human intervention.
There is also a very common one, you probably have one in your house.
Arf arf, I'm the result of selective breeding over hundreds of years, arf arf. [/dork]
If we really came from apes why aren't apes turning or "evolving" into humans nowadays?
Apes aren't turning into humans because:
1) They survive in their environment. That's what evolution is, development over time due to their environment.
2) We did not evolve from Gorillas/Chimpanzees/Monkeys. We share a common ancestor that is long extinct. This is shown through both our DNA and a shared morphed chromosomes [two of the ape chromosomes morphed together into a single chromosome, this is why they have 48 chromosomes (24 pairs) and we have 46 (23 pairs).]
3) Like Crazy Eight said, being a human isn't the end goal. We are human because that's how we survived in our environment.
4) Evolution is very very very slow. If you really wanted to breed a gorilla into a "human" then you'll have to be one dedicated person with many dedicated people after you're dead. First, you'll have to get about a thousand gorillas together, pairing each one up to your desired gene passage. Eventually a gorilla will come along that has less hair then the average gorilla. Another gorilla will come along that can use its rear legs to walk more "up right" then the others. Another gorilla may develop a larger brain capacity. Then you'll have to breed those gorillas with other gorillas, killing the offspring that are like the rest of the gorillas and then breed the gorillas that have their desired mutated gene.
And in about say...a million years of dedicated selection and breeding, you'll have a gorilla that is almost bald, can almost stand-up right, and can hold a pencil in its hand and maybe sing the alphabet.
We've been doing that to wolves for almost 25,000~ years or so, they are a new species called a "dog".