Plenty: Microsoft from 1976-1986, Craigslist from 1995-2004, Oracle from 1978-1984, GitHub from 2007-2012, Atlassian from 2002-2011, probably others. It's pretty common to take external funding sometime before an exit, though, if only because it simplifies finding the exit. (And if the exit is an IPO, you're taking on investors <i>as the exit</i> anyway.)
Of course it's possible. As a co-founder in a startup with a VC funding, now, I'm realizing that doing it without VC funding can be even better idea. It only depends what you want to do.<p>If you want to make some IoT, where you have to buy some hardware, or something that is not only software, you'll probably need some money (like Uber). Levelsio once twitted this - <a href="https://twitter.com/levelsio/status/633405876225896448" rel="nofollow">https://twitter.com/levelsio/status/633405876225896448</a>. I completely agree with that.<p>Start without funding, write something small, with one feature and check if people like it. Iterate quickly, get product/market fit. If it's good and somebody will use it, VC will find you.