Depends. I'm a great believer in picking my battles (and am a lazy cow too) so I do give in sometimes but only if it's something
a) not dangerous
b) not strongly held conviction
c) no big deal
so for example if ds (who is nearly 11) said "can we go out for pizza for supper?" and I said "no because we've got chicken ready to cook" then I wouldn't give in as a result of pestering. But if he said "couldn't we have that tomorrow" and I wanted to go and it actually wasn't a bad idea then I might say "Ok, let's" - I think it's ok to change your mind sometimes. What I DON'T think is ok is to teach them that pestering and going on means you back down on important things.
So for eg, if dd (4yo) won't do a wee before we go out I might say "that's fine, we won't go then" and in that example I won't back down as I want to be sure of no accidents for example (less relevant now but especially important when she was 3 ish).
So I think there's a big difference between changing your mind, which is perfectly ok and sensible and allows children to have their opinions and GIVING IN, which is teaching them that whining gets them what they want.
I do pick my battles with dd, who is highly strung. She gets inordinately upset if I use a tone of voice she doesn't like so it's MUCH easier to say "I am sorry you didn't like my tone, I was just upset that you did xxx" than to say "well, I'M CROSS".
So my children know that I will sometimes change my mind but as a result of reason and discussion, not because they moaned at me. As dd said to me when I was moaning about something the other day "well, you don't always get what you want and bad behaviour doesn't get you what you want" - so the message is obviously ingrained!