The one he wears every day. The one that only gets washed when you can sneak it away when he’s in the bath or asleep. The one he’ll sit in front of the dryer for, waiting and waiting for. The one that is too small and in tatters because he just can’t bear to throw it away.
Actually it’s too big, but it’s a Lego Darth Vader t-shirt. She wears it whenever possible. She’s 6.
For my son, it is the pants I made him for Halloween. They are purple and yellow particolored fleece and already too short. Currently my daughter’s is a very full blue skirt I made her this summer. It is taking the place of a denim circle skirt edged in white eyelet lace I made her three years ago. I can’t begin to convey how much it pleases me that my children love the things I make them.
My sister in law bought cheesy “future cow girl” t-shirts for all three of my girls. My youngest twin signals when it’s time for actual sleep by saying “cow girl” and means to get one of the three shirts on. It’s a rare night when we don’t go through the routine. Good thing we have 3 shirts.
My 4 year old (boy) has a pair of pajamas that have ocean critters printed on them. The Ocean Jammies trump any other pajamas and frequently he will ask to wear them all day.
My 3 year old (girl) has a pink velvet long sleeved romper with embroidered rosebuds. Is it for day wear? pajamas? I have no idea. But she thinks it’s the most wonderful article of clothing ever, and when she has it on, she pats it lovingly and says, “It’s beautiful isn’t it Momma?”
My daughter (7) has a New England Patriots sweatshirt and hat that she wears daily, as well as a MN Vikings Favre shirt that she loves. She was Brett Favre for “hero day” at school. She also loves her Buzz Lightyear pajamas and will wear the pajama pants all day on the weekends.
My son (5) is just starting to get more interested in clothing. He has a pair of green sweatpants that he loves, but for a while they were for Mondays only. 
He has some shirts that he likes, but nothing that really fits the level of attachment described in the OP. Mostly he chooses his shirts based on what he thinks the girls in his class will like to see on him.
My stepson has a black hat with the “Fallen” logo on it. I almost don’t recognize him when he’s outside without it.
He’s, uh, 12.
My almost-3-year-old son has a Cubs hat he wears pretty much all the time. He falls asleep with it at night, even, and if it falls off (or I take it off), he looks for it as soon as he wakes up. The only place he doesn’t wear it is at the table, because his daycare provider taught him that it’s not polite! 
I have a backup hat for the times it gets misplaced, which has come in pretty handy. I make sure I always know where at least one of them is at all times.
My 10-year-old stepdaughter has a really fun batik dolphin t-shirt my brother bought her for Christmas this year. She wears a school uniform and we have her change as soon as she gets home…out comes the dolphin shirt, every time!
My 12 year old daughter: none.
My 15 year old son: his gray hoodie with the high school logo on it. It’s beginning to frighten me.
Funny - my son had a pair of pants he called his Friday pants, only he tried to wear them every day. They had penguins on them. We never figured out where Friday came into it.
His current favorite is a pajama set with skulls and crossbones - his pirate pajamas. He’s 3 1/2.
I don’t even HAVE any kids and this thread is making me tear up.