This seems a bit too obvious to be correct to me, but I'm going to say you're a:
closed puzzle/riddle on Puzzling.SE, probably with the catch-all "lateral thinking" tag people put on just about anything.
You put me up, They tear me down
Some may laugh like I was a clown.
You got posted and quickly closed, most likely for being "too broad". Laughter is still common in these cases, because the premise of these puzzles is often ridicilous.
Fix me up and put me back,
Perhaps now we're more on track.
You'd like to be edited and reopened. Then you'll be "on track" to get answers.
Crazy and impossible things,
All sorts of silly strings.
I'm not sure this needs much explanation. Have you seen some of the posts here? Infinite rope, prisoners that all have perfect logic/memory...
The answer is often clear,
Why my reputation do you smear?
The OP almost always thinks his own question is clear, no matter if it is or not, so get offended (smeared) by the downvotes that often accompany votes to close.
Think about it, puzzle it out,
What this riddle is all about.
I already did that. I think.
Maybe not the way you think,
What am I? Don't let hopes sink.
"Not the way you think" is almost literally "lateral thinking". Please don't let the hopes of having a well received post die...