There is a slew of dataloggers out there that enable museum staff to monitor temperature and relative humidity of collections storage and exhibition spaces. Some dataloggers are networked and push alerts and other information to the staff; others require retrieving the data from stand-alone devices by a number of different means.
To me this the biggest factor in mold prevention is daily monitoring to make sure that within any 48 hour period, conditions have not risen to the levels that encourage growth of mold. In my institution, we are primarily using IPI’s PEM2 devices in combination with Invensys systems data.
In my experience, working together with facilities staff to take advantage of the systems already in place as part of the HVAC is an important step in the protection of collections as well as separate space monitoring.
You could consult the National Park Service Conserve-o-gram for an overview, with the caveat that there are new products coming into the market every year so the products listed are not the most recent, but the information about them in general is still good: http://www.nps.gov/museum/publications/conserveogram/03-03.pdf