Thorium fission:
http://en.wikipedia.org/wiki/Thorium_fuel_cycle
Thorium reactors are in fact breeder reactors, using small quantities of U233 or other neutron sources to breed U233 from Th232. The technical challenges of building such reactors are not small.
If solid fuel is used then the problem is that U232 is also produced by the breeding process. U232 decay products emit gamma radiation and therefore the fuel requires remote handling and processing, increasing fuel and disposal costs. If liquid fuel is used then the solutions are corrosive, which increases the cost of building the reactor vessel by an order of magnitude or more, and increases both the likelihood and severity of nuclear accidents.
U233 can be weaponized, leading to proliferation problems, although the cost of doing so makes U235 and Pu239 the preferred materials for the purpose.
Breeder reactors (including the above thorium reactors):
http://en.wikipedia.org/wiki/Breeder_reactor
The other possibility is to use small quantities of Pu239 to breed Pu239 from U238. Since the Pu239 can easily be weaponized the proliferation problem with such reactors is great.
BTW, all reactors breed; the ratio of fuel produced to fuel consumed is roughly 0.55 in modern reactors. To achieve a true breeder reactor the ratio has to be equal to or greater than one.
There are two main difficulties. First, water cannot be used as a coolant because it absorbs neutrons; most breeders are cooled by liquid metal solutions, with corresponding increases in expense and complexity. Second, the reaction process produces neutron-absorbing isotopes as well, necessitating the removal and reproccessing of the fuel at regular intervals.
The point is that it's all well and good to say that by building breeder reactors we could make more efficient use of our uranium and thorium stocks and gain a few hundred years more for nuclear fission power generation, but doing so is not a simple or cheap process. There are numerous technical and political challenges to overcome before making that a reality.