There's nothing like the scientific thrill of discovering something for the very first time—or, in rare cases, rediscovering something that most people had presumed forever lost. Take the Cuban solenodon (Solenodon cubanus), for example. Unseen after 1890 and long presumed extinct, it unexpectedly showed up again in 1974. Sightings after that were few and far between but scientists kept looking. Last year, after a 10-year search, an international team led by Rafael Borroto-Páez rediscovered the solenodon in a remote mountain park, a finding that thrilled scientists on both sides of the globe.

Unfortunately, most similar quests to find presumed-extinct species don't have such happy endings. In some cases the lost creatures are rediscovered, but even in those rare cases the findings usually come barely in time: Only a few dozen members of the species remain, tucked into tiny habitats facing increasing pressures from encroaching civilization. More often than not the quests remain quixotic: endless, lonely and fruitless. That doesn't stop the scientists or other explorers. Sometimes they keep hunting for decades, looking in every odd corner they can reach, keening at every step for success.

Here are four species that, in all likelihood, are long-since extinct but which people still seek, even though the chances of rediscovery are slim:

1. The Thylacine, or Tasmanian Tiger (Thylacinus cynocephalus)

The last known thylacine died in Hobart Zoo in Tasmania in 1936 after decades of needless persecution by farmers who mistakenly thought the wide-jawed beasts would kill off their sheep. Today, nearly 80 years after the last thylacine passed away, people still search the remote wilds of Tasmania for signs that it might still exist. An Australian magazine even offered a $1.25-million bounty for proof that the species still lived in remote regions, and a Tasmanian businessman offered a $1.8-million reward. Hundreds of people have gone looking, and bits and pieces of "evidence" have turned up from time to time. Most recently two brothers came across a strange skull that they claimed had to have come from a thylacine. No such luck: it turned out to be a dog skull.

The quest for the thylacine is so powerful and so emotional that it has made its way into fiction several times recently, most notably in the 2001 novel The Hunter by Julia Leigh, which was adapted in 2011 into an excellent film starring Willem Dafoe. Much less effective was the awful 2008 horror film Dying Breed starring Saw screenwriter and actor, Leigh Whannell. The Tasmanian tiger deserved better.

2. The Japanese Wolf (Canis lupus hodophilax)

It has been 108 years since the last verified sighting of a wolf in Japan. The Japanese, or Honshu, wolf, a prominent element of the country's folklore, went extinct in 1905 after nearly two decades of decline. The wolf could kill and eat animals many times its size, but it couldn't withstand the threat of rabies, which first emerged in Japan in 1732.

Although the Japanese wolf has been gone for more than a century, people still report seeing or hearing the animals. Some people take those sightings more seriously than others. One man, Hiroshi Yagi, has been searching for the wolves for the past 40 years after he heard a howl one night when he was 19 years old.

Yagi has been all over Japan looking for the wolf and even managed to take some photos of one supposed animal in 1996. (It could have been a feral dog.) His long quest has the earmarks of an obsession, and it has not been joyous. "Through my searches, I have felt the sinfulness of humans," Yagi told Asahi Shumbum last year, a sentiment that may as well be the Extinction Countdown motto.

3. The Ivory-Billed Woodpecker (Campephilus principalis)

Was that the call of the long-lost ivory-billed woodpecker coming out of an Arkansas forest in 2004? The birds had disappeared decades earlier, after logging devastated their habitat in the 19th century. A few birds turned up now and again in the 20th century, but the last confirmed sighting took place in 1944.

That didn't stop people from looking, though, and sightings kept turning up, including a photo (contested by many) that was taken in 1971.

After the Cornell Lab of Ornithology released the recorded call of a lone male woodpecker in 2004, several very public expeditions went in search of the birds. The lab established a $50,000 reward for conclusive proof of the species's continued existence. Alas, after years of searching amidst a bit of media frenzy, no woodpeckers have ever been discovered.

Is the ivory-billed woodpecker still out there? A July 2001 paper in Conservation Biology calculated the odds at less than one in 10,000 but suggested that scientists keep looking. After all, a slim chance is still a chance.

4. The Slender-Billed Curlew (Numenius tenuirostris)

Now here's one where the odds are slightly more in the quester's favor. The slender-billed curlew once migrated between regions around the Mediterranean and Siberia but disappeared decades ago due to habitat loss and possibly pollution. They didn't completely vanish, however. Twenty birds showed up in Italy in 1995, and a single curlew turned up in England—far outside its historic range—in 1998. This may or may not have been a slender-billed curlew, though, and scientists have been fighting about its identification ever since.

A few other sightings showed more promise. In 2009 a team of volunteers combed out across 35 countries on three continents in search of the slender-billed curlew. The search, unfortunately, proved fruitless. But as with so many species that are missing and presumed lost, hope remains eternal.

Photos: Two thylacines at the National Zoo via the Smithsonian Institution archives; Honshu wolf museum specimen by Katuuya via Wikimedia Commons. Used under Creative Commons license; Ivory-billed woodpecker painting by John James Audubon. Public domain; Slender-billed curlew by Elizabeth Gould and Edward Lear from their 1830 book, The Birds of Europe. Public domain.