Great question.  There are many textbook answers to this question – evaluating the market, technology, profitability, team required, financing required (is that financing available), etc.  You can, however, easily get all of that from somewhere else.   Before you even arrive at that point, you need to look deep into yourself and ask yourself if you really have what it takes to go at it alone, live in a world of tremendous uncertainty, perhaps go without any income for a while, etc.  Are you passionate about what it is you are about to embark on?  Would you do it regardless of how much money you might make?  Is your family supportive of you making this leap?  Are you concerned it may not work?
You are the only one who can answer those questions, but I can offer some guidance on a few.  First of all, don’t be afraid of failure.  Failure is an incredible teacher.  Our culture of innovation in America rewards failure with the clear opportunity to try again.   Almost no one is successful in everything they try.   If you are passionate about what you are doing, a failure is not nearly so painful.  
Don’t restrict yourself to starting a business that may be a venture deal – most businesses don’t require and will never get venture capital.  Many of the wealthiest people I have met in my life started businesses you see everyday, built them out of customer receipts and never required, nor did they want, venture capital.
I leave you with a true short story – a story of two grandparents of mine – one in Cuneo, Italy and one a German immigrant in Chicago.  Both wanted for years to start their own business; they both saw it as a way to provide a better life for their families and future generations.  Both were in the baking/candy business.  The German worked long hours in difficult conditions in bakeries in Chicago, planning for years to one day open his own bakery.  He was an incredible baker, loved every minute of it despite the awful hours.  He even went as far as finding locations, lining up bank financing, etc.  However, when it came time to pull it all together, he was consumed with doubt and fear about whether or not it would be successful.  He never opened his bakery and died with his dream unfulfilled.   The Italian grandfather in Northern Italy was equally passionate about candy.  He always said if he could make candy and just give it away making no money and still support his family, he would do it.  It was in his blood.  He also dreamed of one day opening his own candy store to give his family and future generations a better life.  He decided, despite the long odds of success, that even if it barely got by, it was better to have built something his children could work with him on and eventually inherit than to miss the opportunity.  He went ahead and opened a small fledgling store front on the square in Cuneo.  After several years of just getting by, he stumbled upon the idea of putting liquor in chocolates and eventually ended up with a contract to exclusively supply the King of Italy (yes, this was a while ago).  He became fabulously wealthy (unfortunately, future generations squandered it; I never got a chance at it, but that is another post).  Yes, luck played a huge role, but, as we all know, you create your own luck.  He wasn’t any smarter, didn’t have any more money, or a secret formula.  He just went ahead and did it – he got “in the game” as they say.  You never know where an opportunity or business will take you, but if you don’t try, iterate, and iterate again, you will always wonder.
As the founder of Atari (yes, I am dating myself) said when he was asked the same question about starting a company – his response was “it doesn’t matter what the business you start is, just get off your butt and start something.”
John Burke

Thanks for the very thoughtful response, John. It just seems to me that every venture idea has been done already, and a Google search for almost any idea I have has some sort of website already providing or servicing the idea.

Griff87, the fact that someone already has implemented your idea is a good thing.  It means there's a market and room for competition.  Maybe you have a unique twist on the idea and can dominate a niche, or maybe you can simply improve on the competitor's offering.  Execution usually is more important than the idea itself.  For inspiration, search for blog posts on "ideas vs. execution".