The short answer: as often as possible.
Every blog post that you publish is like a doorway into your site: it's a way for potential customers to find you via search engines. The more blog posts you publish, the more doors. The more doors, the more visitors.
Here's a graph from marketing automation company HubSpot that proves the point. They took data from over 13,000 customers, measuring the number of monthly blog posts against the amount of traffic received. The more blog posts published, the greater the traffic:
Courtesy HubSpot
Note the sharp rise in traffic once companies begin publishing about eight or twelve posts per month, which works out to about two or three posts per week (think Monday/Wednesday/Friday).
This also passes the common sense test: when you visit a blog that's updated less than once a week, you get the sense that no one is home. Even worse is companies that have a flurry of blog activity, then quit. Because most blog posts are datestamped, this sends a strong message that your company is one that starts work, but is not able to see it through.
In contrast, if your blog is updated several times a week, it sends a few strong messages. One is that your company is financially strong enough to pay people to blog for you.
Another message is consistency. A regularly updated blog says, "We are a company that delivers good work consistently." It is a signal that your company is reliable.
Also, the more you post, the more you learn. Each blog post is like a mini-experiment to see what resonates with your customers. Over time, some of these blog posts will rise to the top, generating consistent leads for your business. The more experiments you put out there, the more chances you have to win. Here's the data:
Courtesy HubSpot
There's one other benefit from posting frequently: it tells search engines that your site is "fresh." This means the search engines visit your site more often, your content gets indexed more regularly, and all those blog posts show up in more search results.
How often should you publish? The slightly longer answer: as often as possible, but eight to twelve blog posts per month is a good place to start.
Next: The best day to publish!