There are a large number of microbes that are useful to us and have engineering applications. Here are 3 examples of classes of microorganisms:
1.) Bacteria: find applications in all aspects of biotechnology. Some of the very common applications include making of curd (or yogurt), wastewater treatment (by activated sludge process, trickling filters, membrane bioreactors, etc.), pharmaceutical, etc. They are also useful for metal remediation, groundwater and subsurface cleanup and bioenergy production. Some commonly used bacteria include, Shewanella oneidensis MR-1 (for bioremediation), Lactobacillus spp. (yogurt making, etc.), Nitrosomonas europaea (wastewater treatment).
2.) Algae: It is being increasingly considered as a viable source of biofuel. Some other applications include, agar (derived from red algae) for bacterial growth, alginic acid (gelling agent in food), as fertilizers and soil conditioners, etc.
3) Fungi: Among the various applications, bread making and mushrooms are the most prominent. Baker's yeast is used for making breads. Some other applications include, bioremediation and use in pharmaceutical industry.
Hope this helps.