[QuantumClue (OP)]

Apparently Japanese scientists will approach this possibility, and hope to achieve this within only five years!

http://www.stardrive.org/index.php?option=com_content&view=article&id=3146:researchers-aim-to-resurrect-mammoth-in-five-years&catid=45:weird-desk&Itemid=103

[CliffordK]

The Mammoths and Mastodons will be one of the big challenges of the 21^st century...  And likely will be overcome in the early 21^st century.

The advantage of Mammoths over other species is:

• We have a close relative, the Elephants as a "roadmap", and as a host for carrying the young.
• Many Mammoths were frozen in the permafrost, and have remained largely intact for 30,000+ years.  So, it in a sense, it is like putting them in deep freeze.  Thus, we have access to large amounts of DNA

It still won't be an easy task, as there won't be any intact chromosomes, rather the DNA will be mostly recovered in fragments.  The fragments will have to be reassembled and spliced to rebuild the chromosomes.  Then, injected into an Elephant egg, and one just hopes. 

As far as Dinosaurs, DNA is the big issue.

Jurassic Park speculated that some Dino DNA could be indefinitely preserved in Amber.  I'm not sure where that process is.  Perhaps the first dinosaur to resurrect will be a Dino-Mosquito  [xx(] 

There has been recent research into demineralizing dinosaur fossils, which has revealed some presumably original organic tissue, presumably primarily connective tissue proteins.  The proteins can be sequenced to determine the DNA that created them.  However, there are millions of proteins, so if we sequence a dozen proteins found only in dinosaur bones, then we will still be a long ways from cloning a whole dinosaur.  De mineralizing teeth might be another thing to try, as they usually have a higher density than ordinary bone.

Another approach would be to try to analyse the dinosaur offspring, and try to predict the mutations that led to their development.  For example, birds and modern reptiles may both have descended from dinosaurs.  So, they may lead to a common ancestor.  However, such an approach would involve more recreation than actually bringing the past back to life.

A second species that may be brought back to life this century is the Neanderthals.  In fact, there is rapid progress on decoding the Neanderthal Genome.
http://news.nationalgeographic.com/news/2009/02/090212-neanderthal-genome.html

But, cloning the Neanderthals would still be a monumental task.
http://www.cbsnews.com/stories/2010/02/12/tech/main6201715.shtml