Jeff once said that everyone, including moderators, are asked for CAPTCHAs in case their account gets compromised. With that being said you will see less of them after you reach 10,000 reputation.
Personally, I think that once you reach a certain reputation you should never see them as long as you are not posting something obviously automated such as 10 questions per second. The reasoning behind that is that while it's true that if a high rep account gets compromised the website can be spammed automatically, the CAPTCHAs are a huge pain in the ass and the relatively low chance of that occurring is not worth the hassle. Especially because all posts by a certain user past a certain date could be cleaned automatically as well, and because let's face it - it's just as easy for spammers to fill in the CAPTCHA manually.
Also, let's not talk about the "special" decision of wanting to make failed post attempts count as real posts for CAPTCHA purposes.