So basically, Dolly the sheep was an accident. They were trying to clone sheep cells, and they ended up unintentally generating an embryo, which turned out to be viable, hence we got Dolly.
The method they used proved unsuccessful in primates, and the risk of cloning primates (and thus humans) outweighs the benefits (because there really aren't any real benefits, scientifically speaking), so they don't do it.
Where it's most likely to be used is in agriculture, cloning livestock embryos.
What they use cloning for is stem cells. Cloning adult cells to create stem cells means they don't need embryonic stem cells, which is probably the most important thing that came from cloning research in the past 25 years.
The reason it was so important was that it proved that you didn't need an embryonic cell to clone live animals. The nucleus of an adult cell contains all the DNA you need to clone, because Dolly was cloned from an adult cell, which was previously unheard of. Now they know that adults cells can be reprogrammed back to an embryonic stage, and was a major breakthrough for stem cell research.
So basically, we don't hear about cloning anymore because they aren't doing anything that is so exciting it will capture the world's interest, like Dolly did. But it was a major scientific breakthrough that is still very important.
