Scientist's cannot clone dinosaurs at this time, but the ability to do so is likely to be developed in the near future. To clone a dinosaur of any of the multitude of species categorized under the taxonomic superorder classification of Dinosauria requires an intact specimen of their DNA (deoxyribonucleic acid). While DNA is a very strong and resilient macro-molecule, its ability to survive the death of the organism it provided the genetic code for is "only" about ten thousand years. As the last dinosaur species became extinct approximately 65 million years ago, if we disregard the avian species we share our world with, the likelihood of obtaining viable DNA is as close to zero as you can get.
This means that we are incapable of cloning dinosaurs at this time, with our current biotechnological capabilities. Dinosaur blood samples obtained from blood-sucking insects found in amber, dinosaur carcases given up by ancient glacial ice melting or fossilized in ancient tar pits, will not contain viable DNA, despite the wishes of many "Jurassic Park" enthusiasts. It is, however, conceivable that we may be able to determine individual dinosaur species' genomes from such samples using current biotechnological processes, such as polymerase chain reaction (PCR), but we do not have the ability to repair such DNA samples to make them viable for cloning as yet.
The genetic engineering we are currently capable of revolves around inserting or removing genes from viable genetic material or replacing the alleles found at gene locii, not rebuilding that material virtually from scratch. But this does involve the use of retroviruses and cellular mechanisms that manipulate and repair DNA molecules, and our knowledge and abilities in these areas are steadily increasing.
While we are not currently capable of procuring a DNA sample of an individual animal that we would classify as a dinosaur that would be usable for developing a clone, we are likely to be able to in the future by repairing the damaged, non-viable DNA samples procured. Considering the advances in our understanding of DNA and genes since Watson and Crick first offered their model for DNA in 1953, doing so might not be that far off.
The problems in cloning a dinosaur don't end there, however. We have yet to develop artificial wombs that can successfully gestate young. Once we have successfully recreated the genetic material for a dinosaur, we would need some means to gestate it to the point of egg-laying. Logically, this would require using an extant reptile species as the surrogate "mother"; as dinosaurs fall under the taxonomic class Reptilia, and the closer the surrogate mother is to the clone, the more likely a successful outcome.
The reptile species currently sharing Earth with us are considerably smaller than those most of us envision when we think of dinosaurs. Their ability to act as surrogates for brontosauri or that old favorite Tyrannosaurus Rex is highly unlikely, although being egg-layers makes it more possible than might be realized when comparing adult sizes. With sufficient advances in our biotechnological capabilities, it is quite possible that we may be able to clone smaller dinosaur species within the next 50 years, if we decide to do so.