The Hubble Space Telescope is uniquely able to study planets that are observed to transit their parent stars. The extremely stable platform afforded by an orbiting spacecraft, free from the contaminating effects of the Earth's atmosphere, enables HST to conduct ultra-high precision photometry and spectroscopy of known transiting extrasolar planet systems. Among HST's list of successful observations of the first such system, HD 209458, are (1) the first detection of the atmosphere of an extrasolar planet, (2) the determination that gas is escaping from the planet, and (3) a search for Earth-sized satellites and circumplanetary rings. Numerous widefield, ground-based transit surveys are poised to uncover a gaggle of new worlds for which HST may undertake similar studies, such as the newly-discovered planet TrES-1. With regard to the future of Hubble, it must be noted that it is the only observatory in existence capable of confirming transits of Earth-like planets that may be detected by NASA's Kepler mission. Kepler could reveal Earth-like transits by the year 2010, but without a servicing mission it is very unlikely that HST would still be in operation.