Research has found that in many cases rescuers are afraid they will become infected by the victim if they do rescue breaths, so they just do nothing. Being wary of infection makes good sense. Remember, the first rule of any rescue is, "Is the scene safe for me?" It's not safe if there is a risk of getting Hepatitis, HIV, or any other infection. One solution is to carry a CPR mask. These are available for a few dollars online and are small enough to fit on your key chain, put in your pocket or purse, or just leave in your glove compartment or pack.
Still, most people will find themselves at the scene of a cardiac emergency without a CPR mask. The other alternative is to do chest compressions only. In other words, omit the rescue breaths entirely. At first this may not seem to make sense, but there is enough oxygen in a person's blood to keep him or her alive for several minutes, and sometimes that's all it takes for the ambulance to get there if you are in a 911 response area. Some CPR instructors teach hands-only or compressions-only CPR and don't bring up the subject of rescue breaths at all.
In a wilderness or remote setting, however, rescuers are not going to arrive for hours, so you will have to do more. My advice? Carry the mask!