Some of my ideas.
More often then not, however, that person will admit that they have simply been "tossing the ideas around in my head for awhile." Perhaps he or she has not had the time to try to flesh the idea out. Or perhaps it is simply too much of a risk to see if the ideas actually hold up to a playtest. As long as it is an "idea" that exists only in the imagination, it works (idea = ideal).
Whatever the case, the simple fact is that there is no shortage of ideas. What the boardgame market (and any other creative art form or industry) craves is an original solution: something that works and does it in a way that separates it from the crowd of other developed ideas that work.
I, too, have plenty of ideas. I write them down so that I won't forget them. Many of those ideas are for board games, and I try to keep track of them, although my filing system cannot keep up. I probably have at least one idea for a game every week, sometimes many more. I have filled many sketchbooks and files with them, and I sometimes go back to them when I'm stuck on a design that I've taken the time to develop. But I just don't have the time to develop them all to a point where I can test their viability, and so I have to prioritize.
And I have to stick with something I've started to develop until it's either clear that it will work or it's clear that it won't. Jumping around too much from idea to idea can mean that I have a lot of underdeveloped ideas. It's true that they are no longer simply "ideas in my head," but they aren't quite there as self-tested prototypes, either. And there is nothing more frustrating for a playtesting group than to bring in not-quite-developed game prototypes with you. A rules question here or there is allowed, but to bring in an untested game in which there are too many discrepancies is frustrating for everyone. The playtesters might feel as if the designer expects them to design the game for him or her (but there are always exceptions, of course).
So I try to write down every idea I have so as not to forget it. Then I try to file it in a place where I can easily locate it again in the future. I might enlist a friend to help me choose the most promising ones to develop (and I might even ask them to co-design, if it is exciting enough for them). And finally, if it just doesn't work, I'm happy to shelve it.
Sometimes, an idea needs time to mature.