Is it safe to pet and interact with stray or alley cats?

I washed my hands twice after feeding and petting them. I ate some cheezits and then freaked out thinking that maybe I can get worms or something from them. Is there any thing I should watch out for or should i just ignore them and avoid them. They are so cute and skinny I am drawn to them. But my safety is mire important I think. I have no health insurance in case something does happen.