Identification tags during the Second World War varied by country, but for the most part they were effective so long as they could be recovered.

The American tags had largely the same information on them that they would have during subsequent conflicts. American tags had: first name, middle initial, last name, serial number, tetanus shot dates, blood type, next of kin and their address, and religious affiliation. American tags were worn around the neck, giving them the nickname "dog tags" that is now applied to just about every form of soldier identification.

German tags were slightly different and were made of a solid disk that had rectangular pieces stamped out in a line across the middle of the tag. This divided the tag into two halves, with the same information being printed on both halves. In the event of a soldier's death, one half would be broken off and left with the body while the other would be returned to the soldier's unit. It was this link with the unit that created problems with the German tags, since the information was linked with records kept with the unit and was not as individualised as American tags. A soldier's replacement unit, serial number, and blood type were what was most commonly listed on German tags.

British and Canadian identity discs were made of metal or pressed fibre and soldiers were given a green one and a red one. These tags had a soldier's name, unit, serial number, and religious affiliation. Though I can't seem to find anything that shows WWII British discs listing blood type.

To answer your question, the tags were designed to help with identifying the bodies of soldiers, but there was only so much they could do. Wearing an identity disc or tag around your neck was more reliable than wearing it around a wrist, though even then it is not difficult to think of scenarios when even necklace tags would not be recoverable. One criticism I've seen of the German identity discs was that they were made of aluminum and zinc, both metals that have a low resistance to heat. In addition, the Soviet Union issued it's soldiers with bakelite (plastic) tubes with their identity inside on a piece of paper. Needless to say, these didn't help much with identification.