Alpha decay and beta decay account for almost all decays of the naturally occurring radioactive isotopes. If an atom suffers alpha decay, its atomic number is decreased by two, and its atomic mass number is decreased by four. A beta decay has the effect of increasing the atomic number by one, while leaving the mass number unchanged. So, any long-lived radioactive element will give birth to a particular sequence of isotopes (i.e., a decay chain) on its way to becoming a stable isotope.

The four major decay chains follow:

Uranium Series
U-238 -> Th-234 -> Pa-234 -> U-234 -> Th-230 -> Ra-226 -> Rn-222 -> Po-218 -> Pb-214 -> Bi-214 -> Po-214 -> Pb-210 -> Bi-210 -> Po-210 -> Pb-206 (stable)

Thorium Series
Th-232 -> Ra-228 -> Ac-228 -> Th-228 -> Ra-224 -> Rn-220 -> Po-216 -> Pb-212 -> Bi-212 -> Po-212 -> Pb-208 (stable)

Actinium Series
U-235 -> Th-231 -> Pa-231 -> Ac-227 -> Th-227 -> Ra-223 -> Rn-219 -> Po-215 -> Pb-211 -> Bi-211 -> Tl-207 -> Pb-207 (stable)

"Neptunium" Series
Am-241 -> Np-237 -> Pa-233 -> U-233 -> Th-229 -> Ra-225 -> Ac-225 -> Fr-221 -> At-217 -> Bi-213 -> Po-213 -> Pb-209 -> Bi-209 (stable)

There are four main decay chains for the heavy isotopes, since the atomic mass number modulo 4 remains invariant under alpha and beta decay. Three of the series are observed in nature, but the Neptunium Series is not, for the simple reason that none of its isotopes naturally occurs.

Any unstable heavy isotope that does not appear in one of these main decay chains either undergoes spontaneous fission, or soon joins a chain through alpha or beta decay, since the isotopes listed are the most stable for a given atomic number, or for a given mass, and so are energetically favorable.

For example, in a breeder reactor, U-238 undergoes neutron capture to become U-239. This ultimately decays by U-239 -> Np-239 -> Pu-239 -> U-235, and then follows the Actinium Series. (Of course, Pu-239 has a half-life measured in tens of thousands of years, so although it is fairly unstable, it is considered the end product of a breeder reactor.)

Neutron capture allows the isotope to switch decay chains. The fourth decay chain is accessed by the reactions:
Pu-239 + n -> Pu-240
Pu-240 + n -> Pu-241
Pu-241 -> Am-241 + e-

This reaction is of particular interest because Americium-241 is a substance vital to the operation of most smoke detectors.

I obtained the decay product information from some very useful web pages provided by Lawrence Berkeley National Laboratory. In constructing these decay chains I include only steps occurring with probability greater than 95 percent.