Years ago I faced the same issue. I decided to tell my boss and he actually supported me with advice and mentorship (he ended up convincing me not to quit, but that's another story...)
The first question that comes to my mind is: Do you really need to quit? Having an income while you moonlight is a huge advantage, as you can survive until your start-up is sustainable (and then quit your day job)
Second: Do you have enough savings to survive a year on your own? If not, keep your current job, build your savings and then quit.
Third: Are you in good terms with your immediate manager? If yes, then do tell him/her -- You might be able to even negotiate an alternative deal, like part-time, contracting or something else. If not, then tell him/her only if asked. In any case, it's certainly better to learn the news through you than through someone else.
Obviously, what I wrote in this post does not apply if you and your employer have a conflict of interests. If that's the case, I'd talk to a lawyer.
Fortunately I was working for a startup that had a great exit when it was acquired. Since they were entrepreneurs themselves they were amazingly supportive and I still go to the founders for guidance from time to time.
For more on this topic - I wrote a post on how to break up with a girlfriend (or employer) that addresses how to not burn your bridges at:
If it's to pursue what you love and have a passion for, then telling your current employer your quitting to essentially pursue happiness should be absolutely no big deal. :P
I would keep pretty hush about it unless there's some real chance your employer is going to say "Wow that's cool -- why don't you partner with me and I'll invest $5M."
People can get petty and weird when they're jealous or angry.
Ask them to sign a form (user dhouston had done this) where they say that projects you work on in your free time are your own copyright. It depends on what you signed when you were hired. They may not own anything if you didn't sign anything.
The first question that comes to my mind is: Do you really need to quit? Having an income while you moonlight is a huge advantage, as you can survive until your start-up is sustainable (and then quit your day job)
Second: Do you have enough savings to survive a year on your own? If not, keep your current job, build your savings and then quit.
Third: Are you in good terms with your immediate manager? If yes, then do tell him/her -- You might be able to even negotiate an alternative deal, like part-time, contracting or something else. If not, then tell him/her only if asked. In any case, it's certainly better to learn the news through you than through someone else.
Obviously, what I wrote in this post does not apply if you and your employer have a conflict of interests. If that's the case, I'd talk to a lawyer.