While most aircraft have upward-pointing winglets
there are also some UAVs (I couldn't find any manned aircraft$^1$) with downward pointing winglets.
I'm pretty sure that other considerations such as ground clearance, propeller/camera system protection and stability were the determining factors in the examples showed above.
However, according to a study (p.11) referenced in this question downward-pointing winglets are more efficient.
This also means that winglets sticking up are not as efficient as folding them down.
I couldn't find the sources mentioned in the paper.
What makes downward pointing winglets more efficient? What are the efficiency-related differences between the two directions?
$^1$: No, neither the A-10's nor similar wingtips count.