In short, by uploading to instagram, you retain copyright. But you grant them an unlimited license to do what the hell they want with it, sell it, distribute it, whatever, which is actually worse, because any problems arising from their use of the image are actually the problem of the copyright-holder, ie you.
Imagine you take a photo on a street, and there's random strangers in it. You post it to instagram. Instagram then take the image without telling you, and sell it to some advertising firm, who use it on billboards across the country. The people in this photo take offence, and sue the advertising company, who say "we bought it from instagram", so they sue instagram, who say "we just have a license, the copyright holder is this guy, go sue him", and you're at the end of the chain.
Problem is, there's no way to prevent any of that. You won't even know instagram have sold it until you see it on a billboard, or worse yet, when the lawyers come knocking. Only way around it is to not use instagram. Or most places, facebook do it too. I haven't posted an image to facebook in years, not even a link to my smugmug.
Anyway, after that story broke, there was a massive backlash, from the few people who bother readings terms and conditions and spreading the word. Instagram then promised to 'back down' and 'remove the wrong wording'. They did change something, but the gist was still the same last time i read it. In short, don't use it. Then I got bored of trying to 'help' my friends not get legally boned, using it makes them happy and if they get bitten in the ass at least I've tried to warn them.
As for 'proper' photo-hosting sites like flickr, smugmug, zenfolio, their terms and conditions are a lot more on your side, but that wont stop theft. And even if someone does steal your stuff, and you're legally in the right, it's a hassle to chase people down and get it back, especially in countries with dodgy (or missing) legal systems. If you're afraid, just don't post them on the net, don't get the exposure, and don't sell as much.
(and then there's the counterpoint to all that, summed up nicely here with the quote "it seems like many amateur [photographers] spend more time putting elaborate watermarks on their images than they do making images worth stealing").