Seems like most child or teen actors grow up fine and aren’t burnouts. The few burnouts like Todd Bridges or Susan Olsen are the exception and not typical.
Some of the child actors like Gary Coleman had money troubles, but that was mostly his parents mismanagement.
Helen Hunt
Anna Paquin
Michael J. Fox
Jeremy Gelbwaks and Lisa Gerritsen got the hell out of showbiz and have apparently lived very productive lives.
If you grade such people based on how famous they were when very young, how sexualised and fucked up their early roles were, and how together they are and always have been in adulthood, Jodie wins hands down in my book.
Jodie fan? Moi? What made you think that?
You tried to shoot a US president?
Lukas Haas has done okay … did some partying in his 20s, but nothing “fucked up” AFAIK – and gets occasional work (recently seen early in “Lincoln”), despite having once said he didn’t plan on being an adult actor. Not sure if he has some other, steadier job these days as well.
P.S. Diego, it’s a good thing you were careful with your punctuation – otherwise, you could get Princhester in trouble! 
Scarlett Johansson began acting in films at age 9. AFAIK, she’s OK – she certainly looks OK. 
One of them (Mary-Kate?) developed a major eating disorder. I don’t follow their progress so I don’t know how she’s doing now, but she was worryingly skeletal for a long time.
Last I checked the Fanning girls (Dakota and Elle) seemed to be doing okay. Have I missed a front page story of a drug-addled underage sex romp or anything?
Yes there have been a few hiccups. Its remarkable that Downey survived.
Still too young to be out of the woods, but Daniel Radcliffe (Harry Potter) seems to be doing quite well. Taking interesting roles in film and theater, getting OK to good reviews, and seems pretty normal in interviews.
The OP mentioned the HP three (although IMO Emma Watson comes across as a bit big-headed in interviews - YMMV).
Radcliffe is, I think, a bit of a nerd at heart which probably helps; there’s a YouTube clip of him singing Tom Lehrer’s The Elements to a baffled Graham Norton and he positively kicked ass on QI with some very esoteric knowledge of magic. And Grint seems reasonably mellow although who knows.
Also featuring Jackie Earle Haley, who started acting on the big screen at eleven; at twelve he was showing up for episodes of The Partridge Family and Marcus Welby, at thirteen he was playing a juvenile delinquent on SHAZAM, and at fourteen you’ve got Day Of The Locust and Bad News Bears…
…and in his forties, he makes a sudden comeback, earning an Oscar nomination before playing everything from Rorschach to Freddy Krueger; there were some lean years in between, but apparently no trainwrecks on the way to turning fifty in time for Dark Shadows and Lincoln, with Robocop on the way.
Tatum O’Neal straightened herself out? No snark, I’m really asking. I thought she’d recently had yet another relapse.
I’ve already forgotten whether or not she’s already been mentioned: Brooke Shields.
See also: Seth Green.
Susan Olsen? Cindy Brady? She’s not a train wreck.
I’ll add Diane and Erin Murphy, who played Tabitha on Bewitched.
**Jenny Lewis **(Troop Beverly Hills, The Wizard) is a very successful musician now (solo and also with Rilo Kiley).
Kirsten Dunst. I never thought she and her round Charlie Brown head would translate into an adult actor. She’s in her 30’s now and working very steadily.
Yeah, she’s working but I also hear a lot of drug rumors about her (cocaine).
Melissa Gilbert had a very well-publicized battle with alcohol and drug abuse.
Its been nine years now since all of that. Now things are going well for her and Ashley as far as I know. 
God bless you and them always!!!
Holly (a day one fan of them)