There are three fundamentally different forms of decays: the ones involving the weak force where flavors are changed, the ones where the number of nucleons inside the nucleus gets changed, and the one where only the energy level changes.
The best known decays belonging to the first group are the beta and the positron decay. All the decays where a heavy quark or lepton decays into a lighter version, also belong to this group.
In the second group, the alpha decay is the best known. In this decay a heavy nucleus emits a helium nucleus. The original nucleus gets changed, but there is still the same total number of each protons and neutrons in the end. Similarly, there are decays where a proton or a neutron gets kicked out of the nucleus (watch out, the term neutron decay is sometimes also used for the beta decay!)
In the gamma decay, only the energy level changes. An energetic nucleus can get rid of its excess energy by releasing a high energy photon.
More about weak decays and other decays on the main page.
About Decay in German. (Zerfall)