This is a tricky issue, because of course it should be important, but first you have to define it correctly. In theory, checking for culture fit means considering whether any potential job hire shares your company's vision, attitudes and values. In practice, it can be deflected into more personal channels, and you end up choosing new team members based on shared personal history or hockey team preferences.
All too often, and especially in vibrant tech startups, the choice ends up in hiring someone who seems to fit in socially and intellectually, but in fact has nothing particularly innovative to offer, doesn't share your core values, and won't really help your company growth. It may work in the short term, and you may enjoy a lively and friendly working environment, but will it help you succeed in business? For that reason, it's important to define what your company's vision and values really are.
Vision and Values
It's easier to follow a predefined code than a nebulous idea of, 'well s/he seems really cool, and we get on great'. Getting on socially is not necessary for getting on in business, although it is a bonus if the other criteria are met. Initially you need a core value definition that you can stick to, like the frequently mentioned concept of 'radical candor'. This is something that you can thrash out with your colleagues at the inception of your business life – who are we and what exactly do we believe in? These visions may expand as the company grows, but it's important not to lose sight of what made you gel in the first place.
You need to be ruthlessly honest (hence the radical candor tag), and determine what each member of your team has to contribute to the team effort – and how those contributions will push your business forward into a successful outcome. What motivates them to come to work every day, and how does this gel into a corporate culture? It's not about working barefoot (as they did at Apple) or wearing branded t-shirts like Intimate.io, but about your collective aspirations and values.
Passion or Profit?
How much would you sacrifice to follow your vision? If you have the right blend of core values, they should outweigh your financial aspirations in the event of any conflict. If you feel that you would have to sell yourself morally short to close a deal, for example, would you do it? (If the answer is yes, then you probably have the wrong core values!)
Consider then how any potential hire might respond to these questions, and you might get some idea of whether or not they are a good cultural fit. A good starting point is to design your interviews around your company's core values, rather than focusing solely on academic and social background. Of course you want to share energy, passion, informality and information, and you want to enjoy your work, but you must always remember that it is work, and not play.