There are quite a few teams currently trying hard to detect moons around known exoplanets. The main approach they're using is to search for tiny perturbations in the times at which gas giants transit their host stars, caused by the gravitational pull of an unseen moon. Although the hypothetical signal due to an Earth-mass moon (i.e. a big one) orbiting a Jupiter-mass planet is conceivably within the reach of the ultra-precise Kepler dataset, it's really starting to push it, and to date there have been no secure exomoon detections.

Still, if our own solar system is any guide, there are probably plenty of them out there, and it's just a matter of time before we do start detecting them. One of the appeals of this search is that many exomoons could provide suitable abodes for life, as is discussed in this article. Tidal heating from the nearby planet could even give rise to liquid oceans on moons that are too far from their stars for starlight to melt water, like on Jupiter's moon Europa and Saturn's moon Enceladus. The range of habitable real estate in the galaxy could be very large indeed.