If you are interested in this you should probably check out 37signals.com/rework
as they are considered the most 'popular 'internet' company without any funding at all'
Basecamp, formerly known as 37signals, is a privately held American web application company based in Chicago, Illinois.
When asked 'how much are you worth' their answer is 'we don't know and we don't care'.
It's important to know that Atlassian is considered to be one of those 'old-school companies' that used a Enterprise software license / vendor lock-in model that just would not work today. (Think anti virus software and things like that)
I would not call them a 'startup' at all, they were there when the foundation was being laid, being profitable from year one.
There never is a single silver bullet and in the case of Atlassian it's 1,148 employees multiple products (Jira, BitBucket, Bamboo, FishEye, Clover) and years of hard work.
They received a $60 000 000 investment in 2010 by Accel partners and a $150 000 000 investment in 2014.
Without knowing their exact strategy I think it's safe to assume that they found a nice and a need, and then grew by both expanding their customer base as well as up-selling to their existing customers and more recently switching to a SaaS sales strategy.