Clearly the original expression was "I couldn't care less." But it's at least as common these days to hear people say "I could care less." Of course, this grates terribly on the nerves of some people. Is this an unacceptable faux pas, definitive proof of the speaker's ignorance, or one more sign of tragic societal decline? Or is this just another common peeve about which the peevish need to relax?
The point of the expression is clearly to communicate a lack of concern. If I care not at all about something, it's not possible to care less. Thus, I couldn't care less.
So why might someone say they could care less? Well, it could be intended as sarcasm -- saying one thing and meaning another. Or it could be understood as a type of elliptical expression: I could care less, (but I don't). Either way, it's possible that someone might say "I could care less" and still mean "I don't care at all."
I tend to prefer the original, "I couldn't care less" because it doesn't require any interpretation. I suggest you stick with it. It also reduces the chances that you'll get a citation from a grammar cop. But really, this is just another situation where a little patience and perspective would go a long way. Does it really matter which way someone says it if what they mean is clear?
I'm not saying I don't care. If I didn't, I wouldn't write a blog post about it. I'm just saying I could care a whole lot more.