It is true that in Western countries the medical staff won't trust 100% the blood type given on these identification tags and they certainly won't give you a transfusion by relying only on the information contained on these tags.
However, if you have a rare blood type (like AB-, AB+, A-, B-) and depending on where you are, informing the doctor in charge right from the beginning of your uncommon blood type can allow him to order blood in advance (this can be done on the way to the ER). So, when your blood group comes back from the lab, the blood will be ready right away for transfusion (sometimes they have to get it from another medical facility further away). If they have to, they can give you O- blood, but it is always better to get blood that matches you blood type.
Also, it might be even more helpful in developing countries if no lab tests are available (you never know, you might need it on the day the machine is down!).
So, the bottom line is, it is always a good thing to have your blood type on you (on your bike, in your car, etc.).