My students and I recently had a conversation of lunch about ideas and how to find good ones. In academia we are, for better or worse, very concerned with the ownership of ideas, although in a way that is different from industry with patenting and copyrighting. Essentially, if you are an academic, you want your name to be associated with as many good ideas as possible. The way to get your name associated with an idea is to publish a paper on the idea before anyone else does. If you're lucky, others will even name the idea after you. For example: RSA encryption, which is a really great idea, is named after Ron Rivest, Adi Shamir, and Leonard Adleman; Turing machines are named after Alan Turing; in synthetic biology, we speak of Gibson cloning to refer to a method of cloning popularized by Daniel Gibson. Gibson himself didn't think of that name (I don't think), but it is just easier for everyone else to call it Gibson cloning, so we do.
One of the worst things that can happen to an academic is to get scooped: Someone else publishes on an idea that you are working on, but haven't yet been able to finish off. It is incredibly irritating to have spent so long working on an idea, caring for it, experimenting with it, understanding its context, teaching it to your students and colleagues, getting funding for it, writing about it, and dreaming about it only to see it next to someone else's name in the table of contents of some journal. Even worse, some distant collegue or student forwards it to you in email and says "hey, isn't this similar to what you are working on?".
Here's the problem for academics though: Ideas have lives of their own. (Lots of people call them memes -- although I'd rather not do that here. I think of a meme as more general. The context in which you call something "awesome" or the way you twirl your pencil are memes, but you are not going to publish on them). The point is that ideas come from somewhere: you read about them or they pop up in conversation and then they fester in your head, mutating and mixing with your other ideas. For me, new ideas often come from not correctly understanding other ideas. That is, I'll think I understand something and I'll really figure it out well, and then I'll realize that (a) I got it all wrong but (b) what I have is actually new and interesting anyway (Jung would call me "mutable").
Furthermore, ideas travel like wildfire. I tell my students: if you are talking with a bunch of academics at dinner and a great idea comes up: stay way. That idea is probably stuck in the heads of hundreds of people, and unless your lab is enormous and fantastically funded or you already have a paper on the subject 75% done, you run a high risk of being scooped. In fact, most of research is dominated by herd behavior with academics following trendy ideas to get funding. In fact, it often seems that the ideas control us, and not the other way around. This depressing behavior of ideas might suggest to you that you might want to keep your ideas to yourself -- or among trusted colleagues -- while they are young. But who wants to live not talking about the very ideas that get us up in the morning? Besides, being secretive is also not good for the ideas: you never know when you might talk to someone who knows something about that can help you make progress. Sometimes good ideas need all the help they can get.
In general, academics wanting to own ideas and ideas wanting to be free are really at odds with each other. Probably the best situation for an academic is to be working in a field that no one cares about, or to invent an entirely new field, and then to discover something really cool in that field that has huge impact. Of course, that later creates all sorts of stressful competition (RSA encryption, for example, rendered the formerly sleepy field of number theory somewhat exciting for a while, much to the chagrin of some mathematicians). It is really an uphill battle to work on obscure problems. Nobody knows if what you are doing has any potential use at all. Even you may not know. Funding proposals and papers will get rejected, etc. The work may never pay off: you just have to hope to get lucky and have a "black swan" event. If fame is what you want, skip academia. If care and feeding of interesting and obscure ideas is what you want, research is for you.
So what to do? Be an individual. Avoid herds. Think about your brain is the substrate on which ideas live. Help the ideas and seek out the strangest ones. Don't try to own ideas, try to shepherd them.