My story:
In 1995 I had a technical idea underlying a product, and tried to do it at my current company. It was an uphill slog due to lots of resistance, and it just wasn't happening. Java 1.0 had just come out. My company was thinking about client-side Java (which is how Java was initially positioned). My idea made more sense server-side and I liked Java. I decided that my idea was potentially useful and decided to do it on my own. I gave myself eight months to build something and then figure out what to do with it. I had no idea how to sell it, market it, did zero market research. I have a very understanding wife.
Eight months later, prototype is done and working great, and I had been trying to find interested parties. A tech giant in Redmond was "interested", but only because they were hiring people in my area of expertise. They were going to buy the software to hire me. It was basically a signing bonus. But I visited and could not stand the place.
A friend of a friend put me in touch with a VC who put me in touch with a local startup who bought my software for a decent amount of equity. The startup went on to a good exit and I lived happily ever after.
Obviously, I was extremely lucky. The idea I just had to work on happened to actually have some value. But I just as easily could have been fooling myself. Things are very different now, due to open source, and I think that the path I took wouldn't work any longer. Certainly not for the technology I worked on, (there are now many open source products available), but obviously lots of software that used to be proprietary now isn't.
As for what you should do: Do you have a technical idea, requiring innovative software? (I'm assuming you are a software engineer.) Or do you have a business idea that requires only well-understood technology? If it's the latter, and if you are primarily a techie, the risk of fooling yourself is much higher.
No matter what you do, be very careful about IP issues with your current employer. They can lay claim to anything you do while you are employed. Review your employee agreement and think about whether your idea overlaps anything your company cares about. I suggest talking to a lawyer with some experience in IP and employee agreements if you decide to pursue your idea while employed. (As I was about to sell my software to the startup, my old employer accused me of stealing trade secrets, which nearly killed the deal. They had no basis for the charge -- they were on a fishing expedition. But it made my life miserable for several weeks.)