Usually the heads that come up with ideas for websites that ultimately became successful were programmers in the first place, or originally programmed their website. In fact, I can think of no huge succesful website who's idea came from someone that wasn't in the development process.
The reason for this is that programming a website to get it to run exactly how you want takes a lot of work to originally do, and maintain. So there's no way you can just "hire" a programmer for a day to draft up the website and then keep all the revenue that comes from it; doesn't work like that. If the website is gaining so much traffic that it generates a sizable amount of income, you're going to need maintenance... programming for new features, etc. So yea... you're better off befriending some programmers who'll be in it for the long-run. Oh, and they'll want most of the income since they're doing most of the work.
As far as "stealing" ideas for websites... there's rules to things that you can and can't patent. You should look those up.
A common misunderstanding of this whole "getting rich off a website" idea is that people think that all they have to do is attract a lot of visitors, put some ads on their site, and that will generate revenue. It will; but not on the order of what you're probably looking for. NikeTalk does that and I believe it makes only about $20-$30 a day. The key to wealth is in an information bank. Websites like Google, YouTube, and especially Facebook have information banks collected from their users that are worth gold to advertisers. Sure they make a lot of money because of the visitors they get (you won't, because your website probably won't be as big as any of those), but they're "worth" a lot more than their revenue... and that's because of the information they collect.