We recommend submitting a vector file for any print order as it produces the most optimum results. Although not necessary for all print orders, there are some special orders that do require vector files:
Rubber Stamps artwork
Tissue Paper artwork
3D Embossing files
Die-line files for custom shapes
Files for Embossing, Debossing, and Foiling
The following files are highly recommended to be submitted as vector, but can be produced with high quality raster images when needed:
Separations files for Spot UV
Silk Screen files (including artwork for T-shirts)
Letterpress files
See: What is a vector? What is the difference between a vector and raster file?