Lightest supersymmetric particle

In particle physics, the lightest supersymmetric particle (LSP) is the generic name given to the lightest of the additional hypothetical particles found in supersymmetric models. In models with R-parity conservation, the LSP is stable; in other words, it cannot decay into any Standard Model particle, since all SM particles have the opposite R-parity. There is extensive observational evidence for an additional component of the matter density in the universe, which goes under the name dark matter. The LSP of supersymmetric models is a dark matter candidate and is a weakly interacting massive particle (WIMP).
Constraints on LSP from cosmology.
The LSP is unlikely to be a charged wino, charged higgsino, slepton,
sneutrino, gluino, squark, or gravitino but is most likely a mixture of neutral higgsinos, the bino and the neutral winos, i.e. a neutralino. In particular, if the LSP were charged (and is abundant in our galaxy) such particles would have been captured by the Earth's magnetic field and form heavy hydrogen-like atoms. Searches for anomalous hydrogen in natural water however have been without any evidence for such particles and thus put severe constraints on the existence of a charged LSP.
LSP as a dark matter candidate.
Dark matter particles must be electrically neutral; otherwise they would scatter light and thus not be "dark". They must also almost certainly be non-colored. 
With these constraints, the LSP could be the lightest neutralino, the gravitino, or the lightest sneutrino.
In extra-dimensional theories, there are analogous particles called "LKP"s or "Lightest Kaluza–Klein Particle". These are the stable particles of extra-dimensional theories.