Less-known conjectures of significant influence and the contrary In mathematics, it is common that theorems/results and problems appearing dull in one generation get revitalized and become the center of research in another one.
Sometimes conjectures that are thought to be untouchable become resolved within years.
I would like to know if there were conjectures that did not appeal to a large number of mathematicians but when they were resolved( maybe partially), the techniques used or the result itself touched upon many areas.
On the other hand, are there also conjectures which were expected to have dramatic impact but upon resolution did not meet to that expectation? 
 A: Kummer, in the 1850s, proved the p-th power reciprocity laws for regular primes. He conjectured that his formulation was valid for arbitrary primes, but the only one who mentioned this conjecture and hinted at a way of solving it was his student and friend Kronecker. Only when Hilbert, at the end of the 1890s, proved a quadratic reciprocity law in number fields with even class number did it become clear what to do, and within the next 15 years Furtwängler followed Hilbert's path and proved the full p-th power reciprocity law. These results didn't appeal to many mathematicians, and only when Artin found a way of
formulating the reciprocity law in a conceptual way did it become a widely known and widely used result. 
Certainly one reason why Kummer's conjecture was largely neglected was that the techniques for solving the problem were lacking. In addition, a lot of people probably did not think it was interesting because the problem could not be put into some conceptual framework since Frobenius published his results on the Frobenius automorphism at about the same time Hilbert was working on these problems.
A: One can contrast Hilbert's 7th problem (http://en.wikipedia.org/wiki/Hilbert%27s_seventh_problem) on transcendence with his views on Fermat's last theorem. These are reported somewhere, namely that the 7th problem would be harder to solve, since FLT would probably be solved soon. Now the 7th problem was solved (or at least the better-known part?), and it would be unfair to call the Gelfond–Schneider theorem shallow, but it was only one advance in transcendence theory which required new ideas after that. On the other hand we now know with hindsight that the "modularity theorem" approach to FLT goes really deep; this wasn't something that wasn't at all apparent until about 25 years ago. There might have been a "cheap" proof of FLT that showed that the existing criteria on p did rule out all cases: but something very different happened.
A: An open problem whose solution did not deliver what many people were hoping for was the elementary proof of the prime number theorem.  Although this was a fantastic achievement by Erdos and Selberg, it has not led to further dramatic breakthroughs in number theory, at least not to the extent that many people were hoping.
A: An example of an important solution to a little-known problem might be
Frank P. Ramsey's "On a problem of formal logic" in Proc. London Math.
Soc. 30 (1930) 264-286. The problem was in logic and not well-known even
to logicians, but Ramsey's solution was taken up by combinatorialists 
(notably Erdős and Szekeres) and it grew into the important field now known as
Ramsey theory.
{Added later] An example of the contrary type is Hilbert's fifth problem.
This was a well known and difficult problem, worked on by eminent
mathematicians such as von Neumann and Pontryagin, and it took
more than 50 years to solve. Yet, by the time it was solved it
seemed to be no longer in the mainstream of Lie theory, and books
on Lie theory today make little mention of it.
PS. I agree that this question should be community wiki.
