Personally I think parents should try and be fair, but as some people have pointed out, fair isn't always equal. And I'll put bets that some people can argue even when it is equal.
If you're not dividing it equally then I suspect it is often best to discuss it beforehand (eg if one family has inherited millions from the in laws, and won't notice the 5k that comes from the parents it may be appropriate to leave them less)/ However some people hate discussing money and things like that, and sometimes it may be more appropriate to leave a message explaining the reasoning.
One thing I do think is that wives and husbands shouldn't get involved, or feel they are "owed" things. I know when my grandparents died, one of the wives was very pushy to be at any discussions about dividing things up, and was also pushy about trying to aquire things.
Giving items away can also be seen as unfair-for example one war veteran I know caused bad feeling by giving (when he was alive) his medals to his youngest son. The reason was (and I can understand it) that his youngest son was the only one who had his own children, (and they were all old enough more coming along wasn't on the cards) and he wanted them to stay in the family. The oldest son was annoyed because he felt that he should have had them-but the veteran was pretty certain that they would then pass out of the family, either through being auctioned off, or going to his wife's family.
But when it comes to aunts/cousins/family friends then I think it is fair enough to give to one and not to another. There are perfectly good reasons why they might be closer to one than another. One of my uncles I would say that I'm probably closer to than my siblings, one of my great aunts had a special relationship with my dsis for a very good reason. If she had chosen to leave her something (as far as I'm aware she didn't but she might have done) I would feel it was fair enough.
I think another thing that I've noticed is often the better off, the more grabby they are. Not always. but often the person who is struggling accepts being given little, but the one who has plenty is terribly annoyed by not getting more.