Used advertising for a while, also switched to paying for messages since it was still very profitable with the income from advertising (the reason for getting so many users).
Eventually the cost grew above the income from advertising and I had to cut it off before making a loss. Still made quite a hefty profit out of the things, and did use the user base to launch another 3-4 applications.
The whole thing happened while I was traveling on a gap year post high-school. I know I could have made a lot more out of it if I had decent resources. With a decent advertiser (one that also paid for a small text advert at the end of each sms - even a tiny bit for them), I believe I would have earned 5x-10x the amount I did.
Later sold the thing which was a big mistake, although once the users are no longer active - they had no value. Few days after I sold it Facebook added methods to message all users with the application installed (a bit spammy - but sorry :/). Still regret selling it - big mistake.
Either way, used all the income from the application to launch the startup I'm busy with now :)