Here’s a great list:
http://en.wikipedia.org/wiki/Unsolved_problems_in_physics
A few examples:
Does nature have more than four spacetime dimensions? If so, what is their size?
Are dimensions a fundamental property of the universe or an emergent result of other physical laws? Can we experimentally “see” evidence of higher spatial dimensions?
Are there physical reasons to expect other universes that are fundamentally non-observable?
Why is gravity such a weak force?
What is the heaviest possible stable or metastable nucleus?
How do we unify the three different quantum mechanical fundamental interactions of quantum field theory? As the lightest baryon, are protons absolutely stable? If not, then what is the proton’s half-life?
Why is there far more matter than antimatter in the observable universe?
What is dark matter? Is it related to supersymmetry?
Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics?
What is the mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 50 kelvin?
It is necessary for computational and physical models of the brain, but what causes it, and what role does it play in higher-order processing outside the hippocampus and visual cortex?