Often, because drawer organizers go on the inside of drawers, aesthetics are not the primary end manufacturers are designing for. However, if you see the inside of your drawers often, your drawers are perpetually open, or if you're using drawer organizers for an untraditional purpose, their style may be an important factor.
If you're going for a modern look, selecting clear plastic storage is a good call. This has enhanced benefits; you can see precisely what is inside, allowing for instant ease of use.
If you're hoping the look will be less busy and more traditional, go for a natural wood drawer organizer. It will have the look of a simple, pretty wooden box, and will match a number of styles as well as, certainly, your home's unique aesthetic.
If you have metal accents in your decor, you can choose a steel mesh organizer for a cohesive and minimalistic look.