So many to choice from, Life on other planets, intelligent life and that have visited and still have visited earth. We have used Alien tech and reverse engineered it to make the leaps we have in technology, Wright brothers in 1905 to the SR-71 in 1966? with out some influence? any why has are advancement seemed to have slowed? Why haven't been to Marsh yet other planets yet?
This also goes back to ancient human and how we were around far longer the what is current believed. Alien human hyrids

I have read a few things about String theory.

That black holes are not what scientists believe them to be. I would like to see some lateral thinking on this one, not just the explorative forecasting that scientists use.

More life not of this earth

Strictly speaking, in science, a theory is already backed by evidence. Empirical science, other than maths, cannot prove much, but a theory becomes more and more trusted the more evidence there is and the more helpful it is to figure out other stuff. Something that is just a suggestion of what could become a theory is called hypothesis. In maths, something that has been proven is a theorem, and other than in empirical science, a theorem is deduced logically from axioms and things already proven. In maths, something that may become a theorem is usually called a conjecture, while a hypothesis can be something of which we do not know if it is true, but may be assumed to be true to derive insights or results.

Personally I have a hard time to wish for something to get substantiated or proven where I think it is very unlikely to happen - for example, cold fusion as suggested by @Jnei would be cool to get substantiated but I am very sceptical of the possibility.

What I would like to see get proven (actually proven since both are conjectures) is the N (not) equals NP problem, and the Riemann Hypothesis (which is really a conjecture). In both cases a proof would have incredibly far-reaching consequences for the field since a lot of work has already been done based on what we believe is true: so, we have a lot of proofs that tell us what would be the case if the Riemann Hypothesis was true or if N could be proven to not equal NP.

Multiverse hypothesis

A hypothesis rather than a theory, but cold fusion.

Theory of Branes, it would bury that stupid String theory once and for all.

Multiverse theory. I like the idea that there is a universe out there where every single little thing that someone did differently creates a different universe. From a big war in history going different to one person waking up late so getting in a car accident and killing someone that lives in another universe.
Endless possibilities.

Multiverse , then I know there's a wolverine version of me out there, also a rich happy me , also a handsome me . The list can go on and on and on and on and on and on

Telepathy or ESP