Weighted model counting (WMC) is a well-known inference task onknowledge bases, used for probabilistic inference in graphical models. Weintroduce algebraic model counting (AMC), a generalization of WMC toa semiring structure. We show that AMC generalizes many well-knowntasks in a variety of domains such as probabilistic inference, soft con-straints and network and database analysis. Furthermore, we investigateAMC from a knowledge compilation perspective and show that all AMCtasks can be evaluated usingsd-DNNFcircuits. We identify further char-acteristics of AMC instances that allow for the use of even more succinct circuits.