I like to say yes if it's safe and needed and we have the means, with only occasional wants. That's why I go overboard on holidays, and drive my dh crazy........it's the one time I can indulge their silliest whims and feel fine about it, because it really isn't me.........it's Santa or that bunny doing it!
I do keep limits on "age appropriate" to my mind........but not physical age, more emotional age. My son has never been alone anywhere other than others' houses, the neighborhood and so on. He's never gone to the mall, an amusement park or a gameroom alone yet. I'm a bit paranoid about that.........
He does get indulged a bit on shoes and clothes.............though just in style, not in name.........I do refuse to pay extra for a certain brand. My mother will get them for him for back to school though. He also does get to choose favorite foods in the grocery store and we occasionally let him choose the restaurant if we go out (usually just when we're in the mood for steak, as he almost always chooses that).
Younger DS is shaping up to be a bit more indulged. Older DS didn't actually know you could buy the toys in the stores until he went to school and other kids told him. He really just thought they were there to play with at that time. Younger ds not only knows, but usually gets one.......if not from me, then babysitter will buy it later just from his description of it. She does seem to let him call the shots a lot, and so we have more trouble with him than we did at the same age with our older (who went to daycare from 17 months).
He does understand the differences in "parenting" style, but I sometimes have to remind him who I am!
There really are a lot of indulged kids around. I see them a lot too. It goes so far as to be dangerous at times. I had a kid come to school a few years ago in 20 degree weather with no coat and short sleeves. When I asked about the coat, her mom said she tried to tell her it was cold out, but she didn't want a coat (the child was 4). Another 4 year old had chronic absences. When I asked about it, her grandmother who was raising her said that they would drive her to school but if she didn't want to come, she wouldn't get out of the car. I told her to pick her up and bring her in. She said, "Well, she'll cry". I told her "Nobody ever died from a few tears." Now, my kids would never get away with that kind of stuff, or with disrespect or misbehavior in general. Not that they won't try, but they certainly won't succeed.