Anything can cause irritation/break outs. I stopped wearing make up for years because I couldn't find anything that didn't give me giant zits or didn't melt off my face. The nice thing about shopping at say, CVS or Rite-Aid is that if something breaks me out, I can take it back without being hassled by some snooty sales associate.
The other thing that helped was figuring out what triggered my skin. Cosdna.com has a huge database of makeup and skincare ingredients and ranks known irritants.