There's a bunch, but one example would be Morningstar, the mutual fund review company. Other than some small friends and family money at the beginning ($80k), Joe Mansueto never raised any money, until seventeen years after the founding and it was making substantial money already.

This was in part by selling annual subscriptions, so he got cash in advance from each customer. Even though he lost money for a while by accounting rules, he was cash flow positive after a year.

Dunno about exceeeding a venture-backed competitor, but Atlassian was bootstrapped from 2002 to 2010, when it already had $59M/year in revenue.

Probably most of the fortune 500 companies today were not fueled by venture capital, but some other form of capital.

Microsoft.

Look at Atlassian... $6.2bn valuation on the stock exchange, after an IPO at $5.8bn. Self-funded.

Joel on Software had a decent article about this a long time ago: http://www.joelonsoftware.com/articles/fog0000000056.html

Well not slow, but Plenty of Fish the dating site was a one man show for a while and it never took outside capital. It just sold for $575 MM.

Shopify bootstrapped for a loooong time before eventually accepting venture money.