It really grates on me.
DH is always asking me to remind him to do things. As if I don't have enough stuff of my own to remember! I have just said to him this morning when he asked me to remind him to do something later "I will probably forget too, why don't you put a reminder on your phone?". He was most put out!
I also used to have a friend that I stopped bothering with in the end because each and every time we made plans she'd say "Remind me, or I'll forget", even when she suggested the plans in the first place AND she had a massive diary that she used to take everywhere and write everything else in.
Surely it's just lazy behaviour to expect others to remind you of everything you need to to?