Free plans are marketing,
not that people on free plans will convert to paid plans en masse, but that people who
will start out on paid plans
hear about the product because of how many people are using the free plan. The blog posts, the twitter posts, the conversations over drinks.
How likely is the free plan to work to do that, how do you make it more likely? i don't know. I just recognize the products that have done it. There is of course still a danger in the free plan costing you more than the marketing is worth.
Of then of course, once you become a household term (which would have been hard to do without the free plan), the free plan can be an albatross you'd like to get rid of.
An example which comes to mind is travis, which I don't think would have become nearly as popular without the free plan -- in part because they were kind of introducing the whole market of cloud CI. And of course, the recent new private equity owners of travis just got rid of the free plan, although I don't know how generalizable that particular example is, private equity is almost always about slashing costs at the intentional expense of future growth.
In fact, this now reminds me of recent discussions we've had about open-source centered busineses, like perhaps ElasticSearch. The open source license is what gets you the market share, but then perhaps interferes with your desire to maximize exploitation of that market share. Similar perhaps to what free tiers, at their best, will do.