This can make a huge difference to how your cut turns out. Some papers I have found do just not like the Cameo. I have mainly been cutting 3d Projects and have found that the following papers are cutting well. I have made a little chart and keep it next to my machine with the paper name and a little swatch of the paper stuck on the sheet and then I put the blade depth and speed at which I cut.
Bazzil Basics - Blade 5 Speed 2 - cuts beautifully but do ensure that it is proper Bazzil paper and not a look alike - real bazzil paper generally has a sticker on the back of the sheet.
Curious Metallics Paper 300g - Blade 8 Speed 2
American Traditional Designs textured cardstock - Blade 5 Speed 2 - do remember though that this paper has white core so you may need to go around the edges with an ink pad so that the white doesn't show.
Vellum - Blade 3 Speed 3
Opale Shimmer 250G - Blade 5 Speed 2