What is the most stable conformation (Newman Projection) of CF3CH3?
For $\ce{H3C-CF3}$, the stable conformation is staggered. I would expect this to be case for any similar, freely rotating molecule (the exception being conformations imposed by rings etc.), with the reason being the repulsion between the $\ce{C-F}$ and $\ce{C-H}$ bonds.

To confirm, I have optimized the molecular geometry on different levels of quantum chemistry, starting from a conformer halfway between staggered and eclipsed. In all cases, I have observed convergence to the staggered conformer. The levels are


HF/def2-TZVP
PBE-D3/def2-TZVP
B3LYP-D3/def2-TZVP
PW6B95-D3/def2-TZVP
PW6B95-D3/def2-QZVP




In response to comment: I have performed PW6B95-D3/def2-TZVP optimizations for propene, acetaldehyde, and propanaldehyde (the latter starting from two different conformers). The result is that in all cases, the double bond is eclipsed by a single bond (and two non-equivalent conformers exist for propanaldehyde).