The most important ones are:

- theory of everything. We are certain that our base equations are wrong, but we don't know how to fix them :-)
- full explanation of high-temperature superconductivity. Superconductivity already has a gazillion applications, and doing it in higher temperatures would add a gazillion more, and maybe this theoretical explanation would help us find new high temperature superconducting materials more effectively
- fractional quantum Hall effect 5/2

Other super important ones:

- neutrino mass measurement and explanation

- Physics | 276, 46k, 825
- Natural science | 0, 61k, 2k
- Science | 0, 66k, 2k
- Ciro Santilli's Homepage | 262, 218k, 4k

- Grand Unified Theory | 61