Firstly - don't worry about remembering blood groups. In hospital if we need to give blood (except in dire dire emergencies) we always run screening tests to ensure compatibility of blood. In dire emergencies we give O negative blood which is perfectly acceptable to virtually all of the population on the
For the tiny number of people who will have a reaction the argument is essentially that if you need blood under those circumstances then the risk of not having a transfusion is much much greater than the risk of a minor blood group transfusion reaction and that proper cross matched blood for people with minor group antibodies is often difficult to get so not usually possible in an emergency most of their circulating blood volume is on the floor situation.
If you are interested NZ blood have a useful bit on their website which explain inheritance of blood groups.
www.nzblood.co.nz/Give-blood/About-blood/Inheritance-of-blood-groups
Basically each person has 46 chromosomes - arranged as 23 pairs. We all inherit 23 chromosomes from each parent. This is how sex selection by men comes about as women always have XX as their 23rd pair of chromosomes. Men however have XY. To be a boy you have to get an X from your Mum (you can't get anything else) and a Y from you Dad. To be a girl you get X from your Mother and X from your Dad. I digress.
WRT blood groups there are 3 forms of genetic information A, B and O. A and B are what is known as dominant. This means that even if you only have one copy of that information you will have that blood group. Therefore if you are blood group A you can either have the genetic information A A or A O. The same applies to B (i.e. B B or B O). O is recessive so in order to have blood group O you MUST have two copies of the O information so you can only be O O. Rhesus is also negative (but there are only two kinds of info positive + or negative -). Therefore a Rhesus positive person may be either ++ or +-. But a negative person must be - - .
Therefore without knowing exactly what genes each parent has it is difficult to predict blood group for children which is why we test. It is also a proven fact that there are a number of people in the UK whose biological parents are not actually the people they think they are (non paternity) so it is safer to test the person in front of you.
Clinically knowing that you are rhesus negative is useful for girls, especially when they get to child bearing age as even if they have a termination or early miscarriage they should get anti D injections to prevent them developing Rhesus antibodies which can cause problems for future pregnancy. There is an extensive program to make sure these injections aren't missed but I still bang on about it to my friends Rhesus negative teenagers. No one has a better incentive to look after health than the person concerned.
This is really long but I hope it vaguely makes sense. Someone on here works in a transfusion lab and knows masses more than me so will probably be along to correct me!