Appendix carry has become more and more popular over the last 5 to 10 years. It offers some tangible benefits, such as the ability to more effectively defend the gun in a contact distance fight, access to the gun while seated, and potentially even a bit more speed on the draw. While appendix carry is not for everyone, it should be considered as a viable carry method.
One danger that always gets brought up is the danger of shooting yourself in the leg, or more importantly, the femoral artery. While this is a huge concern, it is mitigated almost completely by a good holster, AND A GOOD REHOLSTERING PROCESS. Melody Lauer of Citizens Defense Research has refined the holstering process. She will visually and physically clear the holster of any obstructions. She then teaches students to put their feet on line and push their hips forward. This naturally bushes your appendix carry holster away from you, and keeps the muzzle from pointing at your body. Then she teaches to SLOWLY slide the gun into the holster, keeping the muzzle oriented outward from your body. That's it.
This is a significantly safer way to holster, and can even be applied to strong hand side. Start by visually and physically clearing any obstructions to the holster. Then bring your feet together, and push hip outward to the strong side. Holster the firearm keeping good control with the muzzle pointed away from the body.
As for the safety in the holster, remember that good gear saves lives. A good holster that completely covers the trigger guard and will not allow anything inside the trigger guard is a absolute MUST. Ensure that the holster has sufficient friction retention to retain the gun in your day to day activities. Finally, please refrain from handling the gun. Many accidents happen when the firearm is handled when it doesn't need to be. Leave it where it is and it will be safer for you and ready when you need it.
Here is a video about appendix carry from Lucky Gunner.