"You accepted an offer already." is a legal reason to bounce your application. So is "You mentioned you're a Cubs fan. We like the Sox." So is "We have no articulable reason at all for not going ahead with you", as long as that lack of reason is not a cover for our true reason, which is that you're black/a woman/a veteran (in certain states)/etc.
You might have a colorable claim for detrimental reliance if it had happened in reverse (Company A withdrew a job offer when they found out you had talked to B, after you had e.g. moved to their city in reliance on their offer), but that doesn't fit the fact pattern you're talking about.
In the future, you should exercise more discretion about what important details of your dealings with unrelated people you share with people you're in a sales situation with. If a company makes a job offer to you, and you accept, but you subsequently don't end up taking a job with them due to them being unable to reach agreement on details of the work, from the perspective of your job search this is a no-op. You have no particular obligation to disclose that fact to people.
Also, you should know that "I recently accepted a job offer, but decided that I didn't actually want to accept it." does not communicate "I am a competent professional who will be a headache-free high-quality productive worker at your organization." That doesn't mean you're forbidden to do it (God knows AmaGooBookSoft would bounce an offer in a hot second if they thought it over and decided "Actually, we have better options"), but again, I would be very discrete on disclosing that in an interview.
They'll might hem and haw a bit, but ultimately, you have an absolute right to not work in jobs you don't want. You'll probably burn your bridges with that decisionmaker, and more than likely with that company, but the world has many companies.
For your future reference, and that of HNers in the peanut gallery: nail down major specifics like this before saying Yes. If you hadn't said Yes already, you'd have an absolutely not-in-the-least-bit awkward opportunity to continue the negotiation and say "That position doesn't sound like what I'd like to be doing. You should offer me a better one, or alternatively, compromise on one of the other levers in this negotiation.", and if that negotiation broke down it would cost you nothing and not leave anyone with a bad taste in their mouths.
Am I interpreting you correctly?
It's totally acceptable to apply to multiple companies and negotiate with multiple offers in hand; you could say to B, "Well, A is offering me ${FOO} a year and two week's vacation, but I'm really excited about the work at B; can you match their offer?" or something like that. But once you accept an offer, it's generally understood that you stop looking for a little while.
It's also totally acceptable to look for a new job while you're working; people get jobs they don't like, or jobs change, and people want something new.
But what it sounds like you've done here is applied at a company, gotten an offer, accepted it, and started looking for new offers immediately. That's unusual, and is definitely setting off some alarms for HR. You're worried that you won't like the job, but there's no way for you to know; you haven't started yet. You're jumping ship before you've even gotten on board; why would B extend an offer to you? How do they know that you won't accept an offer with them and then immediately start talking to C?
The thing to do is to not accept an offer you're not happy with; if one company gets back to you and you're still waiting to hear back from somebody else, it's okay to say "Can I have some time to think about your offer? I'm still waiting to hear back from some other companies, and I want to make sure I have a good understanding of my options before committing". And then you can say to the other companies, "I need a decision from you soon; I have an offer from A and I want to respond in a timely manner to them."
edit: Also what patio11 said; he is eminently qualified to give job-search advice, especially with regards to things like negotiations.
The answer to the question you actually meant to ask is:
When you're given an offer by a company, and you're not sure you're ready to commit to it, because you want to explore other opportunities first, you simply tell the company that gave you the offer that you're not ready to accept.
Your prospective new employer will be candid with you about how long they can hold the position open for. Sometimes it's days, sometimes it's months.
Your prospective employer might, if they're on the ball, ask what you're waiting for and who you're interviewing with. You can tell them, or not tell them. I tend to ask candidates when this comes up, but I only get responses ~50% of the time, and I don't pry.
What you should not do is accept an offer and then continue to interview elsewhere. Accept when you're ready to commit. You can accept, then interview, then accept another offer; it's not unlawful to do that. It's just deeply unprofessional.
Finally: a prospective employer can, for all intents in purposes, withdraw an offer at any time. Not only that: they can hire you and fire you the next day.
